{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 机器学习工程师纳米学位\n",
    "## 模型评价与验证\n",
    "## 项目 1: 预测波士顿房价\n",
    "\n",
    "\n",
    "欢迎来到机器学习工程师纳米学位的第一个项目！在此文件中，有些示例代码已经提供给你，但你还需要实现更多的功能来让项目成功运行。除非有明确要求，你无须修改任何已给出的代码。以**编程练习**开始的标题表示接下来的内容中有需要你必须实现的功能。每一部分都会有详细的指导，需要实现的部分也会在注释中以**TODO**标出。请仔细阅读所有的提示！\n",
    "\n",
    "除了实现代码外，你还**必须**回答一些与项目和实现有关的问题。每一个需要你回答的问题都会以**'问题 X'**为标题。请仔细阅读每个问题，并且在问题后的**'回答'**文字框中写出完整的答案。你的项目将会根据你对问题的回答和撰写代码所实现的功能来进行评分。\n",
    "\n",
    ">**提示：**Code 和 Markdown 区域可通过 **Shift + Enter** 快捷键运行。此外，Markdown可以通过双击进入编辑模式。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第一步. 导入数据\n",
    "在这个项目中，你将利用马萨诸塞州波士顿郊区的房屋信息数据训练和测试一个模型，并对模型的性能和预测能力进行测试。通过该数据训练后的好的模型可以被用来对房屋做特定预测---尤其是对房屋的价值。对于房地产经纪等人的日常工作来说，这样的预测模型被证明非常有价值。\n",
    "\n",
    "此项目的数据集来自[UCI机器学习知识库(数据集已下线)](https://archive.ics.uci.edu/ml/datasets.html)。波士顿房屋这些数据于1978年开始统计，共506个数据点，涵盖了麻省波士顿不同郊区房屋14种特征的信息。本项目对原始数据集做了以下处理：\n",
    "- 有16个`'MEDV'` 值为50.0的数据点被移除。 这很可能是由于这些数据点包含**遗失**或**看不到的值**。\n",
    "- 有1个数据点的 `'RM'` 值为8.78. 这是一个异常值，已经被移除。\n",
    "- 对于本项目，房屋的`'RM'`， `'LSTAT'`，`'PTRATIO'`以及`'MEDV'`特征是必要的，其余不相关特征已经被移除。\n",
    "- `'MEDV'`特征的值已经过必要的数学转换，可以反映35年来市场的通货膨胀效应。\n",
    "\n",
    "运行下面区域的代码以载入波士顿房屋数据集，以及一些此项目所需的Python库。如果成功返回数据集的大小，表示数据集已载入成功。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 载入此项目所需要的库\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import visuals as vs # Supplementary code\n",
    "\n",
    "# 检查你的Python版本\n",
    "from sys import version_info\n",
    "if version_info.major != 2 and version_info.minor != 7:\n",
    "    raise Exception('请使用Python 2.7来完成此项目')\n",
    "    \n",
    "# 让结果在notebook中显示\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Boston housing dataset has 489 data points with 4 variables each.\n"
     ]
    }
   ],
   "source": [
    "# 载入波士顿房屋的数据集\n",
    "data = pd.read_csv('housing.csv')\n",
    "prices = data['MEDV']\n",
    "features = data.drop('MEDV', axis = 1)\n",
    "    \n",
    "# 完成\n",
    "print \"Boston housing dataset has {} data points with {} variables each.\".format(*data.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第二步. 分析数据\n",
    "在项目的第一个部分，你会对波士顿房地产数据进行初步的观察并给出你的分析。通过对数据的探索来熟悉数据可以让你更好地理解和解释你的结果。\n",
    "\n",
    "由于这个项目的最终目标是建立一个预测房屋价值的模型，我们需要将数据集分为**特征(features)**和**目标变量(target variable)**。\n",
    "- **特征** `'RM'`， `'LSTAT'`，和 `'PTRATIO'`，给我们提供了每个数据点的数量相关的信息。\n",
    "- **目标变量**：` 'MEDV'`，是我们希望预测的变量。\n",
    "\n",
    "他们分别被存在`features`和`prices`两个变量名中。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 1：基础统计运算\n",
    "你的第一个编程练习是计算有关波士顿房价的描述统计数据。我们已为你导入了` numpy `，你需要使用这个库来执行必要的计算。这些统计数据对于分析模型的预测结果非常重要的。\n",
    "在下面的代码中，你要做的是：\n",
    "- 计算`prices`中的`'MEDV'`的最小值、最大值、均值、中值和标准差；\n",
    "- 将运算结果储存在相应的变量中。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics for Boston housing dataset:\n",
      "\n",
      "Minimum price: $105,000.00\n",
      "Maximum price: $1,024,800.00\n",
      "Mean price: $454,342.94\n",
      "Median price $438,900.00\n",
      "Standard deviation of prices: $165,171.13\n"
     ]
    }
   ],
   "source": [
    "#TODO 1\n",
    "\n",
    "#目标：计算价值的最小值\n",
    "minimum_price = np.min(prices)\n",
    "\n",
    "#目标：计算价值的最大值\n",
    "maximum_price = np.max(prices)\n",
    "\n",
    "#目标：计算价值的平均值\n",
    "mean_price = np.mean(prices)\n",
    "\n",
    "#目标：计算价值的中值\n",
    "median_price = np.median(prices)\n",
    "\n",
    "#目标：计算价值的标准差\n",
    "std_price =np.std(prices)\n",
    "\n",
    "#目标：输出计算的结果\n",
    "print \"Statistics for Boston housing dataset:\\n\"\n",
    "print \"Minimum price: ${:,.2f}\".format(minimum_price)\n",
    "print \"Maximum price: ${:,.2f}\".format(maximum_price)\n",
    "print \"Mean price: ${:,.2f}\".format(mean_price)\n",
    "print \"Median price ${:,.2f}\".format(median_price)\n",
    "print \"Standard deviation of prices: ${:,.2f}\".format(std_price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 1 - 特征观察\n",
    "\n",
    "如前文所述，本项目中我们关注的是其中三个值:`'RM'`、`'LSTAT'` 和`'PTRATIO'`，对每一个数据点:\n",
    "- `'RM'` 是该地区中每个房屋的平均房间数量；\n",
    "- `'LSTAT'` 是指该地区有多少百分比的业主属于是低收入阶层（有工作但收入微薄）；\n",
    "- `'PTRATIO'` 是该地区的中学和小学里，学生和老师的数目比（`学生/老师`）。\n",
    "\n",
    "_凭直觉，上述三个特征中对每一个来说，你认为增大该特征的数值，`'MEDV'`的值会是**增大**还是**减小**呢？每一个答案都需要你给出理由。_\n",
    "\n",
    "**提示：**你预期一个`'RM'` 值是6的房屋跟`'RM'` 值是7的房屋相比，价值更高还是更低呢？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a6fae10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mKnuLbiAj1Edk7RKaliOI+pxOE86zSgtlW70GU9MziZ5C3O/n0vNXFO5xFOHF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\nkBESQghRGjJCQgghSuN/AyEl47eFYt7bAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a7f2250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7l9yWvapVt7/7PEktoQH7nVO7E8fB4saYPhQoNZRktzdqx61YMj/4e9vtnikN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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a8c3590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def plotScatter(colName):\n",
    "    plt.plot(data[colName],data['MEDV'],'o')\n",
    "    plt.xlabel(colName)\n",
    "    plt.ylabel('MEDV')\n",
    "    plt.show()\n",
    "\n",
    "plotScatter('RM')\n",
    "plotScatter('LSTAT')\n",
    "plotScatter('PTRATIO')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 1 - 回答：\n",
    "\n",
    "从上面三个散点图，从散点的集中趋势，可以猜测：\n",
    "\n",
    "首先，若增大RM的数值，MEDV会增大。这与购买房子的经验是一致的，大房子的总价总是比小房子的总价贵。\n",
    "\n",
    "其次，若增大LSTAT的数值，MEDV会减小。因为低收入者多的地方，消费水平较低，他们负担不起总价较贵的房子。\n",
    "\n",
    "最后，若增大PTRATIO的数值，MEDV可能会减小也可能会增加。从散点图上看不出房价随PTRATIO变化的明显趋势。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 2: 数据分割与重排\n",
    "接下来，你需要把波士顿房屋数据集分成训练和测试两个子集。通常在这个过程中，数据也会被重排列，以消除数据集中由于顺序而产生的偏差。\n",
    "在下面的代码中，你需要\n",
    "\n",
    "使用 `sklearn.model_selection` 中的 `train_test_split`， 将`features`和`prices`的数据都分成用于训练的数据子集和用于测试的数据子集。\n",
    "  - 分割比例为：80%的数据用于训练，20%用于测试；\n",
    "  - 选定一个数值以设定 `train_test_split` 中的 `random_state` ，这会确保结果的一致性；"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO 2\n",
    "\n",
    "# 提示： 导入train_test_split\n",
    "from sklearn.model_selection import train_test_split\n",
    "#train_test_split?\n",
    "X_train, X_test, y_train, y_test = train_test_split(features, \n",
    "                                                    prices,\n",
    "                                                    test_size=0.2,\n",
    "                                                    random_state=2018)\n",
    "#print prices.shape\n",
    "#print X_train.info()\n",
    "#print '=================='\n",
    "#print X_test.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 2 - 训练及测试\n",
    "*将数据集按一定比例分为训练用的数据集和测试用的数据集对学习算法有什么好处？*\n",
    "\n",
    "*如果用模型已经见过的数据，例如部分训练集数据进行测试，又有什么坏处？*\n",
    "\n",
    "**提示：** 如果没有数据来对模型进行测试，会出现什么问题？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 2 - 回答:\n",
    "\n",
    "将数据集分成训练集和测试集的好处：可充分利用好有限的数据资源，如果把全部数据仅用来训练，则会因缺乏测试数据而形成过拟合，导致进入坐井观天的误区。\n",
    "\n",
    "\n",
    "如果用模型已经见过的数据，例如部分训练集数据进行测试。一旦形成过拟合现象，训练出来的模型总是很好地贴合于训练数据。所以无法判别是否发生了过拟合。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第三步. 模型衡量标准\n",
    "在项目的第三步中，你需要了解必要的工具和技巧来让你的模型进行预测。用这些工具和技巧对每一个模型的表现做精确的衡量可以极大地增强你预测的信心。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习3：定义衡量标准\n",
    "如果不能对模型的训练和测试的表现进行量化地评估，我们就很难衡量模型的好坏。通常我们会定义一些衡量标准，这些标准可以通过对某些误差或者拟合程度的计算来得到。在这个项目中，你将通过运算[*决定系数*](http://stattrek.com/statistics/dictionary.aspx?definition=coefficient_of_determination) R<sup>2</sup> 来量化模型的表现。模型的决定系数是回归分析中十分常用的统计信息，经常被当作衡量模型预测能力好坏的标准。\n",
    "\n",
    "R<sup>2</sup>的数值范围从0至1，表示**目标变量**的预测值和实际值之间的相关程度平方的百分比。一个模型的R<sup>2</sup> 值为0还不如直接用**平均值**来预测效果好；而一个R<sup>2</sup> 值为1的模型则可以对目标变量进行完美的预测。从0至1之间的数值，则表示该模型中目标变量中有百分之多少能够用**特征**来解释。_模型也可能出现负值的R<sup>2</sup>，这种情况下模型所做预测有时会比直接计算目标变量的平均值差很多。_\n",
    "\n",
    "在下方代码的 `performance_metric` 函数中，你要实现：\n",
    "- 使用 `sklearn.metrics` 中的 [`r2_score`](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.r2_score.html) 来计算 `y_true` 和 `y_predict`的R<sup>2</sup>值，作为对其表现的评判。\n",
    "- 将他们的表现评分储存到`score`变量中。\n",
    "\n",
    "或 \n",
    "\n",
    "- (可选) 不使用任何外部库，参考[决定系数的定义](https://en.wikipedia.org/wiki/Coefficient_of_determination)进行计算，这也可以帮助你更好的理解决定系数在什么情况下等于0或等于1。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO 3\n",
    "\n",
    "# 提示： 导入r2_score\n",
    "from sklearn.metrics import r2_score\n",
    "#r2_score?\n",
    "def performance_metric(y_true, y_predict):\n",
    "    \"\"\"计算并返回预测值相比于预测值的分数\"\"\"\n",
    "    \n",
    "    score = r2_score(y_true, y_predict)\n",
    "\n",
    "    return score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO 3 可选\n",
    "\n",
    "# 不允许导入任何计算决定系数的库\n",
    "\n",
    "def performance_metric2(y_true, y_predict):\n",
    "    \"\"\"计算并返回预测值相比于预测值的分数\"\"\"\n",
    "    \n",
    "    score = None\n",
    "\n",
    "    return score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 3 - 拟合程度\n",
    "\n",
    "假设一个数据集有五个数据且一个模型做出下列目标变量的预测：\n",
    "\n",
    "| 真实数值 | 预测数值 |\n",
    "| :-------------: | :--------: |\n",
    "| 3.0 | 2.5 |\n",
    "| -0.5 | 0.0 |\n",
    "| 2.0 | 2.1 |\n",
    "| 7.0 | 7.8 |\n",
    "| 4.2 | 5.3 |\n",
    "*你觉得这个模型已成功地描述了目标变量的变化吗？如果成功，请解释为什么，如果没有，也请给出原因。*  \n",
    "\n",
    "**提示**：运行下方的代码，使用`performance_metric`函数来计算模型的决定系数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model has a coefficient of determination, R^2, of 0.923.\n"
     ]
    }
   ],
   "source": [
    "# 计算这个模型的预测结果的决定系数\n",
    "score = performance_metric([3, -0.5, 2, 7, 4.2], [2.5, 0.0, 2.1, 7.8, 5.3])\n",
    "print \"Model has a coefficient of determination, R^2, of {:.3f}.\".format(score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 3 - 回答:\n",
    "\n",
    "R2=0.923表示该模型中目标变量中有92.3%能够用RM,LSTAT,PTRATIO这三个特征来解释。解释比例非常高。这个模型已成功地描述了目标变量的变化。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第四步. 分析模型的表现\n",
    "在项目的第四步，我们来看一下不同参数下，模型在训练集和验证集上的表现。这里，我们专注于一个特定的算法（带剪枝的决策树，但这并不是这个项目的重点），和这个算法的一个参数 `'max_depth'`。用全部训练集训练，选择不同`'max_depth'` 参数，观察这一参数的变化如何影响模型的表现。画出模型的表现来对于分析过程十分有益，这可以让我们看到一些单看结果看不到的行为。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 学习曲线\n",
    "下方区域内的代码会输出四幅图像，它们是一个决策树模型在不同最大深度下的表现。每一条曲线都直观得显示了随着训练数据量的增加，模型学习曲线的在训练集评分和验证集评分的变化，评分使用决定系数R<sup>2</sup>。曲线的阴影区域代表的是该曲线的不确定性（用标准差衡量）。\n",
    "\n",
    "运行下方区域中的代码，并利用输出的图形回答下面的问题。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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94d2DfTmdC+RjM45tw7qktRXuwvar9U8R+Tk2ruYGbLbApnJN/QVWbL8tIr/EJo/Iw/Z9\nNMEYc8Y+1vt3rKvfY861WIV9Lp0L/MwY09wdzjbpNTbGFIvIHOAux4L6J2wCisOBUmPMfGPMyyLy\nF2xM0r2Aa8EajH0GXmWMWS8iLwGLgQ+wVtUjsNan+/b9cBVFUZoOFUlKW8UNdHZTDf8XOAv4s9fS\n4Lw4Hw/chP26ORj7UrAGGxAeccrtcuJJbnXKdsO+KLxGyo8/nf9gBdh5WHeuzdiA65/V1WhjzGYR\nmYJNjfsQkAV8CJzsCRJvdZwX6QnYF6YHsC9PRdgXmoc85f4qIsdiBcLvsMHmW7DC8al93HeFY036\nlYicaIx5qRHtecARN1dhr81ybLrkf1N3XFL6/htyTB9gs3TdiRVIO7Ffzl2xtsnZxk1FXYmNTzrJ\nOOnKnRfBKdjsZI9ghdQH2Ixq3vTf+4KP2skAwIq+M40xvxbbn9Es4Luk0lS/gWMFc+7VM7AC4Xms\nGLwXG+M3cz/b12QYm5L968AvsR9FirAdEQ/CfuRoin0UO/ffz7CZMXtj430+xUkoso/1xpzn0zyn\n3gJs8oyr9vEDQ2P33+TX2Bhzt3P/z8JadCPYZBu3eIrNcOq/APs/XYW1BL9CysXwTWx3Dldjxe4G\n7PN53r60S1EUpamRuj1bFEVR2j4icjT2hWuGMSaTcFA6GE5Mzf+w7nFtyUKrKIqidBDUkqQoSrtB\nRIZjXdXcDntHYy1Cq4F/tGLTlGZERO4APsFaG7pj4wIPxnZGqiiKoihNjookRVHaE5XYTHLfw3aa\nWoyNEbuxGRMhKK2PD5syug82M+CHwClN4LaoKIqiKBlRdztFURRFURRFURQP2pmsoiiKoiiKoiiK\nBxVJiqIoiqIoiqIoHlQkKYqiKIqiKIqieFCRpCiKoiiKoiiK4kFFkqIoiqIoiqIoigcVSYqiKIqi\nKIqiKB5UJCmKoiiKoiiKonhQkaQoiqIoiqIoiuJBRZKiKIqiKIqiKIoHFUmKoiiKoiiKoigeVCQp\nBwwi8lUR2dhMdQ8SESMigeaoX1EUpSOgz2FFUdoLKpIUZR8QkXUi8vVW2O8MEXlHRCpE5PWW3r+i\nKEpboRWfw78QkS9FZLeIrBeRn7R0GxRFaX5UJClK+6IY+CUwr7UboiiKcoDyO+AQY0w+cBRwtoic\n3sptUhSliVGRpDQbzle+60XkfyKyR0R+JyKFIvKSiJSJyL9EpKun/HMislVESkXkTREZ5SwPiciH\nInKVM+8Xkf+IyJy97D9bRBaISImIfAwcmba+j4g8LyLbReQLEbnas+5mEfmziPzJaet/RWSss+5J\nYACwUETKReQGT7XniMgGEdnRHF8XjTH/MsY8C2xu6roVRel46HO4WZ7Dq4wxezyLEsBBTb0fRVFa\nFxVJSnNzBvANYDgwDXgJ+DHQHXv/Xe0p+xIwDOgJ/Bd4GsAYEwHOBeaKyAjgJsAP3LaXff8MGOoM\nxwPnuytExAcsBJYDfYHjgJkicrxn+9OA54AC4A/A30QkaIw5D9gATDPGdDLG/MKzzRTgYKe+OU57\nayEiN4nIrrqGvRyXoihKY9DncAb25znsbFsObARynbYpitKBUJGkNDf3G2O2GWM2AW8Bi40xHxhj\nqoG/Aoe7BY0xjxljypx1NwNjRaSzs24lcKuzzXXAecaY+F72PQO4zRhTbIz5Evi1Z92RQA9jzFxj\nTMQYsxb4LXCWp8wyY8yfjTFR4F4gDEzcyz5vMcZUGmOWY3/4x2YqZIyZZ4zpUtewl30oiqI0Bn0O\nZ2B/nsPGmHlAHvAV4EmgdC9tUhSlnaEiSWlutnmmKzPMd4Kk68Y8EVkjIruBdU6Z7p7yjwODgBeN\nMZ81YN99gC898+s90wOBPmlfDX8MFHrKJLc1xiSwXwz77GWfWz3TFTjHpyiK0oroc7gZMJYPsOfw\nlubYh6IorYeKJKWtcDbWreLrQGfsjzCAeMo8CPw/4HgRmdKAOrcA/T3zAzzTXwJfpH05zDPGnOQp\nk9zWcQvpRyoWyDRg/3UiIj92/OgzDvtTt6Ioyj6iz+F9ew4HsO6EiqJ0IFQkKW2FPKAa2AnkALd7\nV4rIecA44AKs//zjIrK3r4PPAj8Ska4i0g+4yrNuCbBbRG50Aov9IjJaRLxBxeNE5HSxfW7MdNr3\nnrNuGzBkXw4UwBhzu+NHn3GoazunnWHsj7JPRMIiEtzXdiiKonjQ5/BensMi4hORS53jEREZD1wJ\n/Htf26EoSttERZLSVngC64axCfiY1I8gIjIAm/b6u8aYcmPMH4ClwH17qfMWp84vgH9i/cYBcPzo\npwGHOet3AI9iv566/B34NlACnAec7vjFA9wBzHZcRK7blwPeR87DunY8BBztTP+2BfevKErHRZ/D\nDeNbwBqgDHgKuN8ZFEXpQIgx+2WtVpQOiYjcDBxkjDm3tduiKIpyIKLPYUVRWhO1JCmKoiiKoiiK\nonhQkaS0a8R2iJgp6PbHrd02RVGUAwF9DiuK0hFRdztFURRFURRFURQPaklSFEVRFEVRFEXxEGjt\nBuwL3bt3N4MGDWrtZiiKojSYZcuW7TDG9GjtdjQl+ixWFKW90RGfxUrz0C5F0qBBg1i6dGlrN0NR\nFKXBiMj61m5DU6PPYkVR2hsd8VmsNA/qbqcoiqIoiqIoiuJBRZKiKIqiKIqiKIoHFUmKoiiKoiiK\noigeVCQpiqIoiqIoiqJ4aFaRJCKPiUiRiKysY72IyK9F5HMR+Z+IfKVBFa9YAT4fDBoETz/dlE1W\nFEXpcOizWFEURVEaR3NbkhYAJ9Sz/kRgmDNcAjzUoFojETAG1q+HSy7RH2dFUZT6WYA+ixVFURSl\nwTSrSDLGvAkU11PkNOAJY3kP6CIivRu1k4oK+MlP9qOViqIoHRt9FiuKoihK42jtmKS+wJee+Y3O\nslqIyCUislREanfKsWFD87ROURTlwKBpnsXr18Ndd8HKldbCpCiKoijtlNYWSZJhWcZfVmPMI8aY\nI4wxR9RaOWBAU7dLURTlQKJpnsV+P9xwA4wZA337wre/Db/9LaxbB3v2QDTaxM1WFEVRlOYh0Mr7\n3wj098z3AzY3qoasLLjttqZsk6IoyoHG/j+Lc3LgV7+CIUPg5Zdh8WJ44QV49lkrnkaNgokT4aij\n4IgjID8fcnPtMzwUgmCwKY9HURRFUfaL1hZJ/wB+ICJ/BCYApcaYLXvdKhSyXyRFoLAQpk9v7nYq\niqJ0ZPbvWTxggP1Ydc45dvnRR8OuXdb9bulSeP99WLLEWpUeeQQ6d4bx4+0wcSL06GGFVG4udOpk\nx6GQFVAqnhRFUZRWoFlFkog8A3wV6C4iG4GfAUEAY8x84EXgJOBzoAL4XoMqHjPG/vA+8ABcdRX8\n7ndw+eXNcASKoijtn2Z/FqcTDFrh0707jBgBJ5wARUVQXAzLl1sr09tvw6uv2vLDhsHkyVYwjRlj\nBZOI23grnFQ8KYqiKC2ImHYYXHvEEUeYpUuXQiwGhxwC1dX2h7qwsLWbpiiKkhERWZYxjqcdk3wW\nN4RYDEpLYetWKCuz/Stt3gzvvGMF09Kl1iqVlQVHHmmtUZMnW/e9WMyuc2OaRFLiybU+hUKpQVEU\npQ464rNYaR5a291u/wgE4Be/gDPOgLvvtu4e+gOpKIrS9ggEoFs3O1RWws6dViidfjqcfbYVPUuW\nWMH09ttwxx12u169rFiaMsXGM3XpYpcnElY07dgBWxzPQK946tzZxj1lZ1vLlKIoiqI0gvZtSQKb\nZvaoo+CTT+Df/4avfCXlpqEoitJG6IhfLxtlScpEImGtSlu32hgmEWsZCgatlckVTO+8k7I+jRlj\nBdOUKXDooVZ8uSxcCPfea0VTYSFcdpl19evc2Yqz3FwrmvQ3QlEOWPbnWbxs2bKegUDgUWA0rZ8h\nWtl/EsDKWCx20bhx44rSV7ZvSxLYH7u77oJjjoH77rPZlbp1a+1WKYqiKHvD57MCpnNn6zZdUmIF\nTlmZtQJNnw4zZlh3uxUrUqLpoYfgN7+xZSZNsoKpstIKpKoqW/fWrTBvnhVG3/wmfPGF/ajm91tr\nVEGBzcgXDrfuOVAUpd0QCAQe7dWr14gePXqU+Hy+9mdlUGqQSCRk+/btI7du3foocGr6+vYvksD+\nQE6bBs89B2eeCSeeaP3aFUVRlPZBVpZ1rSsshPJym+hh504rbHJz4fDD7XDVVdbq9O67KdH0yiuZ\n66yqsh/PTj01JYYSCVv/zp32I1sgYAVTly5WNKnLtqIodTNaBVLHwefzmR49epRu3bp1dKb1HUMk\ngfVff/llePhhm01p+HB1qVAURWlviEBenh0GDLDJHjZtslamQMAKpi5d7MewE0+0ImrNGjj55Mz1\nbd4Mb7wB48bZWCWfz4qhnBy7PhazWfe2bbPz4bD1RsjPt2UCHednUlGU/canAqlj4VzPjK6THefp\nP2IEfPe78Oij9stiQYFNQasoiqK0T4JBm0a8e3fYs8cmadi2zQqj7GwraETgoIOgTx8riDJxySVW\nHI0aZftmmjAhJZoCATt2iUSsq96mTakYqW7dbJmcHFuPoihKK7B161b/V7/61YMBduzYEfT5fKag\noCAG8OGHH34SDof3KuDOPPPMQT/96U+3jB07trquMnfccUePLl26xC+//PLi/W3zU0891eXWW2/t\nY4whFovJlVdeuW3WrFk79rfelqD9J27wsn69dccYOtT2oTR2rPqbK4rSJtDEDU1EPA67d6dil3w+\nK2Reeglmz07FJIF9/s+ZYwXUkiW2U9sPP7RZ8VzRdOSRKdGUl1d7f9XVNt7JGCuaOne2H+E0CYSi\ntEv251m8fPnydWPHjm34C/78+QXMnduXrVtD9OoVYc6cTVx22X4LD4BZs2b16dSpU3zu3LnbvMsT\niQTGGPxtIKtnZWWlDBw4cMySJUs+GTRoULSyslI+++yz0KGHHlqnQNsbzXF8y5cv7z527NhB6cs7\n1iex/v1tp7JLl8J//pMK1FUURVE6Bn4/dO0KI0faD2F9+0JFhY1N/elPrSASseNbb7VdREyaBNdc\nA089ZX8fHn/c/laEw/Dkk3DppdbCdMYZcOed8PrrVoCBjZXq0sXus3NnK8LWrrWJJJYts65+JSVW\nTCmKorjMn1/AtdcOZMuWEMbAli0hrr12IPPnFzT1rlauXJk1bNiwUWefffaAUaNGjdywYUPwO9/5\nzsDRo0ePOOigg0Zdd911vd2y48aNO/idd97Jjkaj5OXlHXbFFVf0Pfjgg0cedthhh2zatCkAcPXV\nV/eZO3duT7f8FVdc0XfMmDEjBg0aNPrVV1/NBdi9e7fv+OOPH3rwwQePnDZt2uDRo0ePeOedd7K9\n7SouLvYbY+jZs2cMIDs727gCacOGDYHjjjtu6PDhw0cefPDBI1977bVcgNmzZxcOGzZs1LBhw0bd\ndtttPes6vmeffTb/sMMOO2TkyJEjTj755CG7d+9uck3TcdztwH4ZvOoqePppuP9++4WwqEg7mVUU\nRemIhMNWDPXqZUVN165w3HF2XV1JGMJhmDjRDmBFz4cfWkvTkiVWND32mP09GTmypnteXp61HmU7\n7wGuVctNMBEK1UwCEQy2zHlQFKXlufDC/qxcmVPn+uXLc4lEapqaq6p8XHPNIB57LHM8yOjRFTz2\n2Jf70pw1a9aEH3300S+mTp26AeCXv/zlxsLCwng0GmXixIkHL1u2rGTcuHFV3m3Ky8v9X/3qV8se\nfPDBTRdddFG/3/zmN91vv/32rel1G2NYsWLFJ08//XTnuXPn9vnGN77x2bx583r27Nkz+sorr6x5\n9913s6dMmTIyfbu+ffvGjjnmmN39+/c/9Kijjtp9yimnlF500UXFfr+fiy++eOBxxx23+8c//vH2\naDRKWVmZb9GiRTnPPfdct//+97+fxGIxxo0bN+LrX/96WW5ubsJ7fJs2bQrcddddvd96663VeXl5\niRtvvLHX7bff3nPevHm12r4/dCyRBDYOaeZMuPZam/EoKyvVoaCiKIrS8fCmEo9ErGWnuNgmfXC9\nCbKyrEBKjynaF9E0fjwccYQVTbm5qbpiMSuYtjq/09nZNp4qL8+Kpjbg/qIoSguRLpD2tnw/6d+/\nf/XUqVMr3PnHHnus4Mknn+wei8Vk+/btwf/973/Z6SIpHA4nZsyYsRtg3LhxFW+99Van9HoBpk+f\nvgvgqKOOqpg9e3YI4N133+2p+nfPAAAgAElEQVR04403bgWYNGlS5dChQyszbfv888+vW7x4cfZL\nL72Uf++99/Z67bXX8v70pz+tX7x4cd4//vGPtQDBYJCCgoLE66+/njdt2rSSvLy8BMCJJ564a9Gi\nRZ1OOeWU3d7je+211zp9/vnn4SOPPPIQgGg0KuPHjy/fvzNYm44nkvx++Pa3rTXpN79J9Y9xyCEa\ncKsoitLRCYWs90BhoU33XVVl3fFKSqxoisdTqb/D4drZ6zKJpuXLM4umESOslckrmtKTQGzebNth\njF0XDlvBlpVl9x0I2N8td6xCSlHaB3uz+PTpM4YtW2qbs3v3jrBkyaqmbk52dnbCnV6xYkXWww8/\nXLh06dJPunfvHj/ttNMGV1ZW1hJngUAgGZPi9/tNPB7PKODC4XAivUxjchpMmDChcsKECZUXXnjh\nztGjR48G1kMys1yS+ur0Hp8xhqlTp+7+29/+9kWDG7EPdEzV0KMHXH21/UF86inrhrFt2963UxRF\nUToObrrv7t1h2DDrMjd2rJ3u2tWKmF277FBWZufTCYetELrqKiuQli6FJ56AK66wVqQnn4TLLrNC\n6fTTbUzTokXWDS8Usp4Mb71l140ZA0cfDQsW2I93q1fDJ5/AypXWerV0qU0usXw5fPqpjX3atAm2\nb0+1sbLStjORqN1WRVHaDnPmbMIRF0nC4QRz5mxq7l3v2rXLn5ubG+/atWt8/fr1wTfffDO/qfcx\nadKk8meeeaYrwJIlS7LXrl1by2WruLjY99JLLyW/HC1ZsiSnT58+EYCJEyfuvuuuu3oAxGIxiouL\nfccee2zZCy+80LW8vFxKS0t9L7/8cpevfe1rtSxExx57bPnixYs7ffzxxyGw8VErVqxo8g5SO54l\nCewXuWOPtX1oPP647bF9wwbripFTt/uooiiK0oERsaInHLYiCazgqKy0AqSkxIoRN5NddrYVOt4M\ndq5omjDBzqdbmp56qqalqXt32/GtK8C2bIHbbrN1T5tWu43GWLe9aNS2K5Gw8+lZ9IyxVqdQyFql\n3HFWVsoy5bVSaRY+RWlZ3Cx2zZTdrj4mT55cMWzYsKrhw4ePGjBgQPW4ceOa3BXtpptuKpo+ffrg\n4cOHjxwzZkzFQQcdVFlQUBD3ljHGyB133NH78ssvzwqHw4nc3Nz4o48+ug7gkUce2XDBBRcMWrBg\nQQ+/38+DDz647thjj60444wzdh5++OEjAS688MLt48ePr1y5cmUNAdS/f//Ygw8+uH7GjBlDo9Go\nANxyyy2bxowZ06QZdDpWCnAvkYjtXHbGDOtyN3eu/aEYOVLd7hRFaXE0BXg7IRaz4mTPHiuaysr2\nHtfkpbo6JZoWL7bjTOTmwpVXQs+eNQdvjNPeSCSs+2D6kElQBQK1BVUolNnlTwWV0oFp0RTgHZho\nNEo0GpWcnByzYsWKrBNOOGH4unXrVgTbYcKaulKAd0xLEtiH/9ixcPbZ8Pvfw/nnQ79+NqC2T5/W\nbp2iKIrSFgkEbGxRXp7NmtfYuKasrFRyhx/8wMbDZvoYuWcP/OIXtZfn5lqXca9wKiysOd+jh7VE\n+Xx2aMhLiWuRqqqC8vKUwHIFkWs9A1tfunUqGKwppgIB/eCoKAcwpaWl/qlTpw6PxWJijOH+++9f\n3x4FUn10XJEE9oflnHPg73+3P0YLFqTc7hrztU5RFEU5MHHjmtzYJmNSHczu2mVFU7njyeL3p8SF\nS+/eNnlDOn36wMKFNl62qCjz8OGHdpwpViovr7YVKtPgtsXnq50SfeFCuPde6wLYuzfMmmVdAF2L\nVHm5ja2KxWqKKMjs7ucmpfBapdQ6pSgdku7du8c/+uijT1q7Hc1JxxZJ4TAMGgSXXALz5tlg2smT\nbed/o0frVzBFURSlcTQ2rumqq+CWW6wFxyUctoKkUyc7DB1a9/6MsUKlLiFVVGSTPWzfbuOY0unS\nJbN4Wr8ennkmJcA2b4bZs+30tGkpAVQfrjWqutpaxtx59zy57RexdXktU97sfl5Bpb/LiqK0ETq2\nSAL7dezkk+HZZ+Guu2DqVPsw37zZut8piqIoyv7gCoDOne3vijeu6bTTrBB56CFrNSostMLp+OOt\noNhbym+RVB9Qw4bVXS6RsOKsPjH12WewY0dKyKRTVQU33QTPPWfFVZcuVgi60+7QuXNqHAzu3d3P\nGLvPRMIKyV27Um3wWqheegnmz7fnqVcv29/htGkp4eSWE6k5QKpM+ji9bKZtvPV6z3umseviKJKa\n9s4fwMQTcaKJKNF4lGgiil/8BHwB/D5nLH5ELYpKO6Lji6ScnFRK8JkzrVj6znfgyy/tQ75Txn6z\nFEVRFGXfSI9rmj0brrvOCqeqqtRQUVE7c52bZKGxfSf5fFBQYIdDDqm7XDxurV1TpmSOlYrFrKhb\nvdq6EroxWJkQsSnOMwmoukRW5872dzf9ZXnhQuvx4VrctmyBOXPsvk86KXVu6ht72VtZ7zi9LelW\nMK94Kyy0Kd9POKH2dYPUNfP5alrJvPOuxSyTyMo030aEhTGmhgiqjlVTEa2gMlZJZbSSuImDAQQM\nBkGS/d4IAgJZ/ixC/hAhf4hwIEw4ECbgC6iYUtokHV8kgfX9PvJIm7L1/vvh1FNtTJLrdqed9ymK\noijNhTeuKR03oYI7RKMpEVVdbceuS5z35d0VT8Fg4zqh9fttbFV9sVJ//GPN9pWXp/qTct0J3Xgs\nd3rXLmul+vxzW6aiou42BIO1BdTbb9d0SQQ7/4tfWLGZLhzT3fTqW59+nhrzAp4u3rZutfOdOmVO\n4Z5I1ByqqlLT6eu9Vq1MMV8iduyKpXS3xBdegHvusdexTx8rxqdPrymyGjL27Ne1BkXiEaLxKJWx\nSiuEopVUxausCHLwiY+AL0DQHyQ3lItP6rekGWOImzixRIyqWBW7qnYRS8SSgigpqESSYirLn0VW\nICujmAr4DoxXWKX1ODDusLw8+/Vq5kxrRXrkEfjhD+2DfPNm6N+/tVuoKIqiHIi4CRXqi/9JF1Ju\nlrrKyppCyn2pdnFFgffl2mXWLPtSnSlWKr19+fl2GDCg4ccVidQWUV6R5V23dm3doqqkxGYJbEoy\nJZaoS2itXVs71quqyp67119PXbtQyAqxppwPhez5N8beA+44GoX/9/9s1ybu9du0ybonbttW28rl\nwRhD1MSIJmLWGpSIUJGIUkmECqIkSDj9avkwPh8Bf5BAIEQgEKJLIIR4haZPQBLgiwDRpOjK+9tL\ndL/jVwQ2byXWtxc7fnwtZWecgogQwEfA7ycrUHe/n+liKlGVqFdMJQVVfWLq6afhJz+BDRs4FMbs\n7y3UWowfP/7gG2+8ccsZZ5yx2102d+7cnqtXrw4/9dRTG+raLicn5/CKiooP1q1bF7zsssv6v/zy\ny2sz1X333Xd/ecwxx9T5hWPu3Lk9r7322h15eXkJgKlTpx70/PPPf9G9e/c6zM0NY/ny5VkXX3zx\noN27d/sjkYhMmDCh/Jlnnlm/P3U2BQeGSALrJ15WZv3DFyywYql3b9i40X7Fystr7RYqiqIoSm0a\nIqS8ndC6QsoVUO5QVpZ6eT76aBt/5I0BcmOlotH9d/UKhayre48eDSt/7LGZLVs9esBvf2uPJx5P\nHVum6fRl8bg9Fnd6X+pYtSpze6uq4H//s2LQHaJRO27K/ifdBBrpQmrjRtvG9DbdeSeJ5R+SCAWJ\nh4IkQgEifiES9BEJCJGQDxMMkQgFMKEQJiuEhLLIygqTHbLTJhgkEQxgQkFMII4JRMFflRJq7vFl\nuDfy/vUWhffMx1dtrZ/BjVsovHY2bNxI2XFTah9feqwXID4fAewLapY3xkysyx6OxcoAcQxRElRK\ngngiTlxIuer5fBhj6PbKmwyZez++KtvPaBD2kpGk6Zj//vyCuW/O7bu1fGuoV6dekTnHzNl02ZH7\n3pns9OnTdz7zzDMFXpH0/PPPF9x5550bG7L9oEGDopkEUkN5+OGHCy+++OJiVyS98cYbn+9rXV6u\nvPLKAVdfffW2c889dxfAkiVLsve3zlgsRiCwfzLnwBFJ+fm2X4kf/MB2MnvvvXD33dZk/vnnMGZM\nza9siqIoitJeENl7EgVXSLli6qCDbPbXSKS2QHCXuW5h9dXpuv953bfqirWpi7osWzfeCCNGNP58\nNBV1ibc+feDVV2svd8+xVzR5RJSprsZEI5jqaohGIBLFRKohEsFEIhCNYKrd8k4d1c50xJYnGiG4\nbh2ZroqprCT6zlv4qqP4o1GCkSjZ0ViGko3D+P2YrBCJUMiKp1AwKbJM0E4nsoLkLP1fUiC5+Koj\n9LzvEbI/+SzNvc8VPZLy4suURAMwrkByt/Fuj2CElIuieMtAl+dfTAqklmT++/MLrv3ntQOrYlU+\ngC3lW0LX/vPagQD7KpTOO++8kttvv71vZWWlZGdnm1WrVoWKioqC3/zmN8tLS0t9J5xwwkGlpaX+\nWCwmc+bM2eyKDpdVq1aFTjnllGGfffbZR+Xl5XLWWWcNXr16dXjYsGFVVVVVybN2zjnnDFi+fHlu\nVVWVb9q0aSX33Xff5ltvvbVnUVFRcOrUqcO7du0aW7x48eq+ffuOWbp06Se9e/eO3XzzzYVPP/10\nd6ed2+fMmVO0atWq0Iknnjhs/Pjx5UuXLu1UWFgYeeWVVz7v1KlTjS8JRUVFwYEDByZvnPHjx1eC\nFTpXXHFFv9dffz0f4Pzzz9/xk5/8pOjvf/973k033dQ/Ho8zduzYiieeeGJ9dna26du375jvfOc7\nOxYtWpR/6aWXFk2ePLnisssuG1BcXBwIh8OJRx99dP3hhx+e5tdbNweOKhCxbnVVVfC979mvZ+ef\nb8VRZaU1VQ8c2NqtVBRFUZTmwSukshv4odZ18drbkO4O6LXeeEWY2450jj4afvSjmlkAr7gCvvrV\nVD9U7rbeF+30+fRl6eUaQcIkiM28iuCcWxCPeEuEs9h++XfZvXs9hgQJEhhjMMaQwA4mkbDTgQTG\nb0iEDQZjX95NECFo53GSGqQan1xu55w/bp4JZ/lh//0vWdt21GpzrFdP1i98Iu1AEkgkikSjSHUE\niUSQSBRfdaTWMnGW+TIsk+oIvoizvNqpLxJJLg/s2YNUZxYjvsoqOr3xnudADBgQY+wy4zlAr7UK\np0xycJeatDqc7TCpOvCsawYu/PuF/VcWrcwQaGhZvnV5biQRqXHTVcWqfNe8fM2gxz58LKOJdXTP\n0RWPnfbYl3XV2atXr/jYsWP3PP/8853PPffcXY8//njBqaeeWuLz+cjJyUm88MILnxcUFCS2bNkS\nmDBhwiFnn332Ll8dHyfuvvvuntnZ2YnVq1d/vHjx4uzJkyePdNfde++9mwoLC+OxWIyjjjrq4MWL\nF2fPnj276KGHHip84403Vvfu3buG8n7rrbdy/vCHP3RbtmzZJ8YYxo0bN+K4444r6969e3zDhg3h\np556au1RRx21/qSTThryxBNPdL3iiitqiMQrr7xy20knnTT88MMP33PccceVXnnllTu7d+8ev+ee\ne3qsX78+66OPPvo4GAyybds2f0VFhVx66aWD//nPf6469NBDq7/1rW8Nuuuuu3rMmTOnCCAcDieW\nLVu2CmDSpEnDH3nkkfVjxoypfu2113Ivv/zyAe+9997qus5vOgeOSALrVhcKWXH07LM2IPSJJ2y8\n0ubNNog0P7+1W6koiqIobQORxiWGqA/3RbcuoTV8uPX2cNOFpw9Qc9778uxd5oqx9HJuHd5jw4qh\nSCJKdSJKVaKa8lgl5bEKqkwUDu1Bt2vOo//v/0Jo+04iPbqx5XvT2TVxFLKryBpCAPEkLfAb6zJm\n1wmS9E5LF2kZbUF7F3MiFF90NoV3z69htUlkZbHjorPth980UWh8gglnQTgrdew1rC6ZLTiNZfC0\n7xLcWlRreaxXT75IF28tRF1tam7SBdLeljeUGTNmFP/pT3/qeu655+76y1/+UvDoo4+uA0gkEjJz\n5sx+7733Xiefz0dRUVFo48aNgQEDBmQ0Jb799tudrr766iKACRMmVA4fPjwZi/T4448XLFiwoHss\nFpPt27cHly9fHp4wYUJlXW16/fXXO5100km78vPzEwAnn3xyyaJFi/KmT5++q2/fvtVHHXVUJcDh\nhx9esW7duloBaddcc83O0047bfff/va3/IULF3ZZsGBBj48//vjj1157Lf+yyy7bHnQs5IWFhfF3\n3303u1+/ftWHHnpoNcAFF1yw8ze/+U1PoAjgu9/9bglAaWmp74MPPug0ffr0ZEd0kUjjzn2ziyQR\nOQH4FeAHHjXGzEtbPwB4HOjilLnJGPNiszTG57PWpDVrUh38vfYaHHecjUn6/HM49FB1u1MUpUPR\npp7DSpvCGNNy6Za9rnitQDwRJxKrJhKrpipaSVmknD2RcqqildaaY4JAFiFfAUFfgK4SAGNIjBzH\n+isux2vOqWE+SLdWNPV8urhLJCg7Zzp07kz3+x4hsLWIWK+e7LjmIspOPA5MAhIeUWhMzWXe+tJF\nqHffbiKQ9PujnmU7LjyrRkwSQCIrxI4Lz7IxcZnw1re3/TVmvdum732bwnsfruUGuL/UZ/EB6HNP\nnzFbyrfUin/q3al3ZMnFS+oIdts755xzzq7Zs2f3f/vtt3Oqqqp8U6ZMqQB4+OGHC3bu3BlYsWLF\nJ1lZWaZv375jKisr6/1ny/S//+mnn4YeeOCBwmXLln3So0eP+BlnnDGoqqqq3npMPRa7UCiUXOn3\n+01dbRo0aFB05syZO2fOnLlz2LBho5YuXZrtPJ9qVF7fvgDceKl4PE5eXl7s008//bjeDeqhWdWA\niPiB3wDfADYC74vIP4wx3gbPBp41xjwkIiOBF4FBzdaorl2tCPrWt+DJJ20Hs8ccYy1MFRWwYQMM\nGdJsu1cURWlJ2uRzWGlVqmPV7InuobiymJLKEgCyAlnJdMvu2O2zxpstrD0QT8SJxCNUx6upilVR\nVl1GRbSCqljKZc4nPoL+IMFgFl3D7bO/xLILz6XswnObvuIa7m2m5jJ3OmM5Q9nQIdCzJ93veoDA\n5m3E+hSy47orKfuW09dVjXfyNBdJ77iu6boEfT1ly0aNggH96XbbfQQ3bSVqTNOqpTqYc8ycTd6Y\nJIBwIJyYc8ycTftTb+fOnRMTJ04su+iiiwadfvrpSbe10tJSf/fu3aNZWVlm4cKFeZs3b643QcWU\nKVPKn3rqqYJp06aVvf/+++HVq1fnAJSUlPizs7MTBQUF8S+//DLw+uuvd546dWoZQG5ubry0tNTX\nu3fvGnV97WtfK7/wwgsH/fznP99qjOHFF1/sumDBggYniPjzn/+cP23atLKsrCyzYcOGwK5du/wD\nBw6MfP3rX989f/78HieffHKZ62532GGHVW3atCm0cuXKrNGjR1c/8cQT3Y4++uhaCrygoCDRr1+/\nyGOPPdb1wgsvLEkkEixevDh70qRJdVrE0mluk8l44HNjzFoAEfkjcBrg/XE2gOvj1hnIECHZhPj9\nNtPdunVw/fVw+eXW9e6cc6zb3bZt0K2bnVYURWn/tL3nsNKixBIx9kT2UFpVSnFlMdVxGzeSFcgi\nLysPQYglYlTHrXiKJ+IkTMJ2BurGzYggCKFAiCxfbTHVGv3XxBNxquPVROIRKqOVlEfK2RPZkzw+\nt81Bf5CQP0R2cL8TZh0Y7EP8lpeyc6dTdu70JmzQ/vOHQ33cMxO2loN5qGX26SZnaMrsdi5nnXVW\n8fnnnz/0mWeeSQqRiy66qPjEE088aPTo0SNGjRpVMXjw4HoTFFx33XVFZ5111uDhw4ePHDVqVMWY\nMWP2AEyaNKly9OjRFcOGDRs1YMCA6nHjxiWDAs8///wdJ5544rCePXtGFy9enIztmTJlSsXZZ5+9\n8ytf+coIsIkbJk+eXLlq1aoGZRJ8+eWX86+77roBWVlZCYBbbrll44ABA2LXXnvt9tWrV2cdcsgh\nowKBgDn//PO3//jHP94+f/78ddOnTx/qJm647rrrtmeq95lnnll78cUXD7zzzjt7x2Ix+da3vlXc\nGJEkezNb7Q8iciZwgjHmImf+PGCCMeYHnjK9gX8CXYFc4OvGmGUZ6roEuARgwIAB49av34/06bEY\nfPCB7VD2e9+Dzz6zWWry8myAaXW1dburL0uQoihKIxCRZcaYI1phv032HHbKNt2zWGkWEiZBZbSS\nskgZOyt2Uh6x7zgBX4DsYPY+ixhjDLFEzCY0SMSImzjxRLyGy47rvuf2XRPyhwgHwoQD4RoiyrVS\nNcTVL5aIEYlHiMQjVEQqKI9aMRRNRJP79ImPkD9E0B9scpG2cNVC7n3vXraUbaF3Xm9mTZzFtIMz\ndCSrAG3vfC1ctZDZi2anLIkPg9ls9kkFLl++fN3YsWNrZ8xQ2jXLly/vPnbs2EHpy5v7c08dUYk1\n+A6wwBhzj4hMAp4UkdHGmBpOuMaYR4BHAI444oj9U3aBgO0jacsWm170jDNSHcyGQjYD3oYNMHTo\n3utSFEVp2zTZcxia+FmsNBlVsSr2RKwL3a6qXdYSJEJ2IJuu2V2bZB8i1ioDkEXDOwPdVbUr2Rmo\nMSaVzU0g6AuSFchKiqksfxZ+nz9lGYruIRqPOsUFn89H0BckHAiT68ttkuOqj/QX7M1lm5m9aDZA\nqwultiZG3DZlOl8JEhw/9HiqY9VJV0hX+EbiEapj1cllyXWxSHI+uS6Wtl28ukad0Xi0RtnqeDXb\n92yvkTFQURpKc4ukjUB/z3w/artxfB84AcAY866IhIHuOFkqmo2ePW3a71GjanYw26ePzXBXVAQF\nBTaGSVEUpf3Sdp/Dyj4TjUepiFawq2oXxZXFROIREMjyWxc6n7ROcgSwYiog1lpUn5gC6zIXN3HK\nI+WUVpUSN3EMBr/4rYtcIJtOodaLGbrn3XtqxDKBFaQ/f/PnRBNRfOLDJz784sfnc8YZ5usq4/el\n1qeXSZbLUOblz1/m5jduriVGyiPlfG3w14gkrIiIxqN2SNQ/jiQimdenLUvWWcd2a0rWEEvEap2v\nG169gRtevWG/roUghPyhpKj2WivdZTnBHLqEu9RY9ueP/7xf+1UOXJpbJL0PDBORwcAm4Czg7LQy\nG4DjgAUiMgIIAxl9C5uUUMj2ML59O8ycaTuYve8+m8gBrOvdmjXW7a6+Xs4VRVHaNm33OdxMJEyi\nVUVCc5AwCSqiFZRVWxe6PdE9AAT9jlUl1PxWlebA7/Pjxwqi1qSsuoy1JWtZW7KWNSVrWFOyhrUl\na9lSviVj+dLqUn707x+1cCvrpypWxc1v3MzNb9zcJPWF/CGCvqBNcOEL1px3lrn3X74/n6A/yKqd\ndSdt++GkH6ZEjRPPVkPsBFLTyXEgJYSCvuA+ZWJ858t32FymYZZK42lWkWSMiYnID4BXsGllHzPG\nfCQic4Glxph/AD8Efisi12JdQC4wzRko5aWw0Lrc9e4NF1wADz9s+1AaPdoKo+pqWL8ehg1rkeYo\niqI0NW3+OdzEVEQr+KjoIwCyA9lkBbLIDmYnX7oCvkAybqUtCyljDNXxasqryympKqGkqiQZ75MT\nzGkyF7oDCWMMRXuKMoqhoj0po2nQF2RQl0Ec3O1gdlTsSMZ0eSnMLeQPZ/yBhEkkE13ETTw5Hzfx\npNthepm4iZNIpMq7g7tdsq56ytzz7j11HufPj/15DXHjJq5IXxb0Bwn5QjWXOeOGxoulc+zjx2YU\nJH3y+nDJuEsaXV9TMGvirJoxSftHIpFIiM/na5fPR6U2iURCgFqu5dAC/SQ5fW28mLZsjmf6Y2By\nc7cjI+Ew9OgBpaVwySXw3HNw5522g1kRa03audNmuysoaJUmKoqi7C9t+jncxJRVl2GMIT+cTywR\noyJawe7q3bViYgwmmcggy59FdiCbcDCcTCoQ9Fkh1WJ9CJFyoSupKqG4stjG4jgudJ2zOrdoW9oz\nsUSML0u/TAogVxCtLVlbQ/B0CnViaNehTO4/mSFdhzC0YChDugyhf+f+yeQPtYL+gXAgzPVHXU+/\n/H4tfmwuz6x8pk4xMmPUjFZokSWTIAkHwsyaOKvV2uTGad3z7j1sLd+KSexXCvCV27dvH9mjR49S\nFUrtn0QiIdu3b+8MrMy0XntN7d3butwVFNievufOhUWL4Gtfs+tdt7tOndTtTlEUpY1TXFlMOBhO\nZjujnq593K/yZZEySqpKbKY2R0CJ2HGWL8smFPBYpJJCaj++uEPKhW531W52Vu6kImo7vHddmFoz\nFqc1aGwigopoBV+UfFFDBK0pWcP6XeuTme8Aeub2ZEjXIZx28GkM7TqUIV2HMKTrEHrm9tzrtXP3\n39YSJLRFMQJt93xNO3gaxx90PBgYc/OYFftaTywWu2jr1q2Pbt26dTTQdk3RSkNJACtjsdhFmVY2\nawrw5uKII44wS5cubboKV6+GPXusCJrm/CMvXJhKAV5WZsXSsGH71XeAoigHLq2VArw5afJn8X4S\nT8RZunkpXcJdmszqEkvEiCfiRBNR6zKF03+Qm6VNbH9DYb9Nc50dyCYUCNWwSLmdsBpjklnodlbu\npLS6NJm+OjuY3eJxOW0pO1pdFptbj72VyQMms6Z4TQ0XuS9KvmBTWapPTp/4GJA/gCEFQ5JCyB3n\nZeW1xiE1O23p+rUHIvGIFUm9xnS4Z7HSPKhIAiuCPvrIWpNee812MDtnju1g1qW4GA46CLp3b7r9\nKopywKAiqfkpqy7j4+0ft2i8jtt3kJvyOpaIgaFWJ6zhQJhIPGLXC0lR1VoudJlEScgf4rJxlzF5\nwGSMMSRI2LFJ1Jh3lyVIgCE57V1n8GyXNp9p+t5376W0urRWO70d2oIVTq4lyBVCQ7sOZWCXga2e\n/EFp26hIUhqLutuBtRLl50NlJRx7LIwfD/ffD6eeateBXb92rZ3Pqj+lqaIoitLylFWXJa02LYXb\nd1CQujsfdztfzQnmtPPDd4sAACAASURBVGj7IvEIW8q2sHH3xtRQZscri1aSSOsGKxKP8Oslv+bX\nS37dYm3cGwbDj6b8KCmIeuf1btMJN5S2g/t/56YtNxi6hjXhidJwVCS59O0Ln3wC2dmpDmZ/+1uY\n5fj3BgJ2WLcOhg9XtztFUZQ2xo7KHYQD4dZuRi2S8VFNTDwRp2hPUU0RtHsjm8o2sXH3Rrbt2VZD\nCAV8AXp36k2//H61BJKXR6Y9gg/bJ4+IICL4sNPushrzSHLaFTDudPo677yQqu/MZ89k255ttdrS\nJ68PFxx2QZOfu71hjCGaiBJLxJIv2K6F0I1Xc10lG3PcStPjusNG41FiJpZ0h/WJj9xQLt2yu5Eb\nzLVusW3w+aC0XVQkueTnW4EUidgU4KeeajuYPess28Es2OQNxcU20UPPnq3aXEVRFCVFNB6lMlrZ\nJlNj72vsiDGGkqqSWiLIHTaXba6RoEAQeub2pF9+P8b3HU+//H70y+9H37y+9MvvR2GnwmTWtvpS\nNU8dOLXpDr6BXH/U9a2SiKDGC3bCvmAD1iUyECYvlEenUCfCgTB+n7+GC6E3JbfrcumdTyQSSaHl\ndpJbI56NlOhycUMgXDfNpChNE5XutDt/IODttNbrghnwBcgNWjGUE8xJ9avkr9u6qygNQUWSiwj0\n7w+ffWYTOFx7re1g9pe/hF/8IlUuPx+++MKOw/pFQlEUpS3gZoZra6TH/mwu28zsRbMBm3GrPFJe\npwjaVLap1nF1DXelX34/RvYYyTeHfpO++X3pl+eIofy+DbZYtbXsaM2ZFc21Crkv2W5/U5B6we4a\n7kpuKDfZn1DIH2py8eEVV24sVrroctfFE47QclzG3Gl3ecyk1iVMwrbVAJISWj7x4ff58Ykv2S/Y\n/mRjbAnca+W6yHkJB23GR1e0umLIFf6K0tRo4gYviQQsX26z2oVCcM898Mgj8Je/wKhRqXLl5dbq\ndMgh6nanKEqD0MQNzcv6XevZWbmzzaXNPnbBsWwur22xCfqC5AZz2VW9q8by3GBuUvC4lqB++f3o\nl2eXNeXxdbTsaOluVxiSGQizA9nkBnPJDeXWeMFu6Ri25sBr0XJFVNzEicat2KiKVSXPSyQesaLK\nOS/eJCOuoPKLH7/Pnxw3V5u9liGvBS8nkENuKJdOoU5kBbKS16qpYtE64rNYaR5Ufnvx+aw1ac0a\nK5IuvRT+/GeYNy/VwSyk3O6KiqCwsHXbrCiKotj+kVox3qA6Vs360vU1+uz5ouSLjAIJIJqIcsKw\nE2qIoH75/Zo0ffnemHbwtHYnijJZhVxC/hA5wRwKsgtqul35gm3aerK/+MSHz++rN3mIF6+gSroK\nJuJE4hEi8QjV8WoisQhV8aqaljfHUuWO/eJPWqtcQZUuZNyYrmgiSiKRioPz+/zkBHPoEu6StOAd\nCNdKaV+oSEqna1eboCEWs2IoUwezAJ072yQObiyToiiK0ipUxaqIxCPkhnKbfV8llSWs3bWWtSXO\nULyWtbvWsnH3xhrJEPrm9WVw18HkBnPZE91Tq54+eX245au3NHt72yvuy7XrWpaM5REhJ5BD56zO\ntSwNHcEq1BL4fX78+OvtaNnFGFNDUCXd/ZyscV5hVRWpstfKSNLtL8ufRW4ol9xgbrIvMI0XUtoL\nKpLS8fuhXz8rgLp2hRkz4MknbVzS0UenOpj1+621ae1aGDHCWqEURVGUFqep45HiiTibyzanhJDH\nOlRSVZIsF/KHGNxlMKN6jGLa8GnJzksHdRlEdtB+PKurk9TWiv1pC7ixNO6LdzQerZW8IOQPZX65\nVktDiyIiBCTQ4Lgfr6gK+AIqXJV2jYqkTHTrBhs2QDxuRdH118MVV8Bzz8HZZ6fK5eZCSQls2wa9\ne7deexVFUQ5giiuLCflDjY6xqYhWsG7XulpiaN2udbbjSYeC7AKGdB3CN4Z8w3ZiWmA7Mu3Tqc9e\nXwKbMyFBWySTAAKSwsYYg1/8hANhcoI5hAPhZIxQwBdIDvpy3T5prKhSlLaM3sWZCASs6Nm8Gbp0\nsW523g5mO3kCZzt3hvXr7Tgnp/XarCiKcgBijGFX1S4WrVvEnEVzamWRMxgm9ZtkRZDHTe6Lki/Y\nVLYpWY9PfPTP78+QrkOYMmBKsvPSwV0G73da8fYY+5MJNx7IG8vizRQHNlFCugAK+oMEfUEVQIqi\ntCtUJNVFz56waZPNeOfzwQ03wJln2g5mr702Vc7ns6nAP//c9q+kbneKoigtRmWskngizi/f+2UN\nlzawsUo3vHpDjT5VcoI5DO4ymK/0/gpnjjwzKYYGdhnYLB2+ulTHqmv0aQTU6GDUze5V1/zeymQq\n3xjqEkDp+8sKZNUSQAFfICmCVAApitJRUJFUF6EQ9OplO47Nz4cxY2DaNPj9720Hs173upwc63a3\ndWuq41lFURSl2dkT2YMgbCnbknG9wTD76NlWDBUMpTC3sMViWowx7InuIRKL0CmrEz1yegAk+8Nx\np71jg8EYOyRw1jlZweLEbZmEU8bpaydTPcksZA4iqU5Mkx2YuuslJYCyg9lkB7JVACmKcsCjIqk+\nCgthyxYwxqb/njULXnkF7ruvZgezYN3tNmywgqpT2+qnQ1EUpaOys2In4WCY3nm92VxWO912n7w+\nnDf2vBZtUywRo7y6HIOhe053enXr1SKZ97y4ViBXdLnT6euAZu0PR1EUpb2ivmH1EQ5Djx6wx0nf\n2qcPXHAB/P3v8NFHNcv6fNaitHIlrFoFpaXWVU9RFEVpFuKJOKXVpWT5s5g1cVatfpJaOotcdaya\n4spiKqOV9O/cn8N7H87QgqEtLpDAccETSfVj4/MnY4KC/iBBf1BTZyuKotSDiqS90bs3RFJZjrjk\nEpsafN48a2HyEg5DQQFUVsInn/D/2bvzOMnuut7/r08tvfd09yyZzEyWSULIgmBiAgICEgyCaES9\ngCAiCAp6Bb1GvIIgIBcURHL5XS+CgCAubOFeJeEGQUNAUSEEhAAJA8kkk2S6M1svU91d6zmf3x/n\nnOpT3dV71XRX9/v5eNRjqk6dqvpWVc+3zud8P9/Pl298IxqJKpfPbJtFRLaBYq0IRAHBdZdcx1uu\neQtZiw749w/u5y3XvKXtBRPcnenKNOOz45gZl+y6hCv3Xcm+wX1tneMkIiLtpSBpOX19UeCTjCYN\nDsKrXgW33w5f+MLSj+npgQcfjIKl730PTp9eGFiJiMianC6dJmNzP2PPuvhZmBmvuOoV3Pbi29oa\nINXCGhPFCSZLkwx1D/HovY/mB876AUZ6RxraJCIinUk9+Urs3984GvS858HBg9G8pFpt8cflclEJ\n8eHhKMi6664oYHr44cbRKRERWbVTxVP1RVsBTsyeoBbW2D/YvgI6pVqJieIExWqR84bO29CUOhER\naR8FSSsxMBAVZChGqR31BWYPH44WmF2OWbTw7M6dUdW8I0fgP/8Tvv99jS6JiKxBNagyW51tSGlL\n1j1qdZCUpNRNFCfIWIZH7nqkUupERLY4VbdbqQMHonlGvfFZyx/7sbkFZq+7buUV7fL5aE6TO0xP\nw6lT0N0djVaNjERBlIiILGm2Ortg2+jpqLpdq4KkWlijUC4AsKdvD3sH9mrESERkm9BI0krt2BEF\nSEnanVm0wOypU9ECs6u12OjSPfdAoaDRJRGRJUyVpshlGs/zJSXA1xskJSl1pWqpnlJ34c4LFSCJ\niGwjGklaKTM477yoAEN3d7RtqQVmVyOfj+YtuUfpdydPRkUfktGlfL5170NEZAsYL443zEcCGJ0e\nZbhnmL5836qfr77wa1BhoGuAR+56JEM9QyrCICKyTan3X42hoWjUJ1104bd/Owpu3vWu9T+/WZS2\nt3NnVPThvvvg61+He+/V6JKISKxcK1MJKk1HklY7ipSuUjfcPcyjz1KVOhEROQNBkpk908wOmdk9\nZvaaRfZ5npndZWbfMbOPtLtNa5bJwLnnzpUDh2iu0otfDP/wD/CkJ8Gll8I118DNN6/vtbq6olGk\n4eFoYdrvfAfuvBNOnIBqdX3PLSLbypbqh2k+HwlWFyQppU5ERJbS1nQ7M8sC7waeDjwEfNXMbnL3\nu1L7XAy8FvgRd58ws7Pa2aZ1GxmJRnlqtehfiNLwIApgAEZH4fWvj65ft851OpLRJYhGsA4fjrbt\n3g1nnRXNazJb32uIyJa1Ffvh8eI4+WxjGrK7M1oY5YnnPnHRx6VT6ga7Brlk9yXs6N6hESMREVmg\n3XOSHgfc4+6HAczsY8CzgbtS+/wq8G53nwBw9+NtbtP6ZLNwzjlw//1RwATwnvcs3K9UghtuWH+Q\nlNbVFV3cYXIyCsp6eqLRrOHhuaBNRGTOluqH3Z2J0gT9+cYRn6nyFLPVWQ4MHljwGFWpExGR1Vrx\n6TMze6SZ3Wpm345vP8bMXr/Mww4AD6ZuPxRvS3sk8Egz+zcz+7KZPXOlbdowu3ZFqXdBEN0eG2u+\n3+hotODsf/xHaxePTUaXRkaioO3w4Wju0n33NaYCisiWs4a+eEv1w6VaiSAMyGayDduTynb7BvY1\n7KuUOhERWYvV5Bi8nygdowrg7ncCz1/mMc3ywOZXH8gBFwNPBV4AfMDMhhc8kdnLzewOM7vjRJLW\ntlFyuaiSXSE6M7loVbuuLvjrv4aXvCRaU+nlL4cPfzgqxNCqIgxdXdEo0o4dMDEB3/pWNHfp5Mko\nJVBEtprV9sUt64dh4/vi6cp00+3p8t/TlWnGi+NkLcsluy/hin1XaOFXERFZldXkZ/W5++3WOP9l\nuaPwh4BzU7fPAUab7PNld68C95nZIaIf66+md3L39wHvA7j66qs3vszbWWfB0aMQhnD99dEcpFJp\n7v6eHnjLW+BpT4Pbb4cvfSm6fPGL0f3798OP/EhU7OEJT4gq561HJtM4d+nee6MRp7POgj17oK9P\nc5dEtobV9sUt64dh4/vi8eI4PbmeBduTIGlX3y5ymRyX7LpEI0YiIrJmqwmSTprZRcRnIM3sOcAi\neWZ1XwUuNrMLgKNEZzt/Yd4+/0B05vKvzGw3UdrH4VW0a2N0dcHZZ0fzgpJ5RzfcEKXe7dsXBU7J\n9muuiS4ADz4I//ZvUcD0mc/AjTdGAc5jHhMFTE96UrT+0nrmFyVzl8IwWuz22LG57T09c5fu7uh1\ncrloLaZcToGUyOa32r54y/TDoYdMlacY6l54Umm0MEpProfBrkF2dO9QgCQiIuuymiPx3yA6e3ip\nmR0F7gNeuNQD3L1mZq8EPgtkgQ+6+3fM7M3AHe5+U3zfj5vZXUAA/K67n1rDeznz9u6NgiL3KCBa\nSZGGc8+NFp59/vOjUt533jk3yvTud8P//t9R6twTnjAXNO1f4+rxmQwMDs7drtWiy+RkNJ8qmVMF\nUXDkHgVS3d3Rpbc3CqaSQCq5ZFQJSmQDraov3kr98Gx1FnfHmpzMGS2Msm9gH47TlVFanYiIrM+K\ngiQzywBXu/u1ZtYPZNy9sJLHuvstwC3ztr0hdd2B6+NLZ+npiVLZpqbmUt1WI5+Hq66KLr/1W1Hw\n8u//Phc0ffaz0X4XXBAFS09+Mjz2sVHq3FokQU539+L7JMHT6dPRHKcgmBtdSuZR5fNzI1HJqFR6\nNEqBlEhbrLUv3ir9cKFcaBogQRQkHRg8QOjhgvLgIiIiq7WiIMndw/hM5CfcXeXT0vbtm1sfab2G\nh+FZz4ou7tG8oiRguvFG+Ju/mQusklGmSy9tbYpcNhtdupY4E5sEUoVCFNglBSLSwVQSjPX0NB+R\nyucVSIms0nbvi8eL4/Tlm58kGi2Mctnuy3CcXEbLIYiIyPqs5pfkn8zs1cDHgfqPs7uPt7xVnaSv\nD3bujEpv97cwB94MHvGI6PKSl0C5DHfcMRc0/emfRpfdu6MCEEkRiF275p7j5psXnye1HisJpMIw\nCp6mp6ORtlptLqUvkctFAVRvb/TZdXdHwVNyEZFmtmVfXAtrTFemGekdWXBfqVbiVPEU+wb3YW4L\nyoOLiIis1mqCpJfG//5GapsDF7auOR1q/3749rdbGyTN1909Fwz93u9FxRiS1Lx/+Rf41Kei/S6/\nPNonk4nKjScV90ZHowp80NoFbheTycwVkFhMEkhNTDSOxrlHj58fQHV1zQVQKjAh29e27Itnq7OL\n3pcu/41B1hQkiYjI+qw4SHL3C9rZkI42MBAVWygWo4P6M2HvXvjZn40uYQh33TU3yvShDzVfI6lU\ngre/HZ74xCi1L7vBBxJLBVLuUWGLQgHGx+dGoNyjAClJ4+vri/5NB1BK45MtbLv2xVOlqUXT6MYK\nUXG/A4MHwNFIkoiIrNuKgyQzywO/Djwl3vQF4C/idTXknHOiQOVMBUlpmQz8wA9El1/7tSjF7aqr\nmu974kQUJJlFazPt2hWlC6Yvu3bByEjjfa0MqlaSBmi2dABVq8HsbJTKlxSXSAKp7u654KmvrzGA\n2ujAUGSdtmtfvNj6SDA3krRvcJ9GkkREpCVWk273HiAP/Hl8+0Xxtl9pdaM60uBgdEBeLi9dPe5M\nGBiIUgBH568XSRT8vOpV0fpJ4+Nzl3vuibZNTTXOG0qYRYFSs6AqHVwl14eGmgckN9/cuPDuWtIA\nzeaCnmZBaa0WPX+hsHAuVD7fGECl50GtZ20qkTNn2/XFlaBCqVZqOh8J4GjhKBnLsLd/L9OVaY0k\niYjIuq3mqPCx7v6DqdufN7NvtrpBHcsMzjsPDh2KRjhg4UKtZ9L11zcGIxClqL3udUsHI8k6SuPj\nUdA0MTF3PR1Ufe970b+Tk82fJ5OZC6pGRuaCqJtuamwTRLff+c7WzZVKPveeJmedgyBK45udhYcf\nbgygstkoeErWierpmfvustm559V8KNlY264vnqksXchvrDDG3v695DI5MpYhY0q5FRGR9VnNkXtg\nZhe5+70AZnYh0aKDkhgehiuvhEpl7kB8Zib6txAvZZIcYCfBU7vm0CQBx2qr2+VyUcW83btX9jrV\n6lxQlb7MD6q++90o4CossqTL2Bg87nFRQJW+7NzZ/PrISDRittqAJanMN3+0L50CePbZ8Bu/AU9/\n+tz96dG1ZMHd5N90MJUOqBRMSXtsu754ojix5NpHo4VR9g/uJ/CArqwWkhURkfVbTZD0u8BtZnYY\nMOB84Jfb0qpOlp5HM5JKDQnDKHhKLknwNDMzlxKWSJfBXs+B9nXXtb+SXT4fLai7Z8/K9n/qU6NA\nZL7BQfipn5obuTp6NKoYODERBWKLvfbw8MoCquR2szlO81MAx8bgLW+Jgp9mn1+yTlRS3jyYd3ya\nBFTpYCpZfFfBlKzftuqL3Z2J0sSi6yNBlG535b4rtZCsiIi0zGqq291qZhcDlxD9MH/X3ctta9lW\nk8lEB8pJClh6pKZWmxt9KpXmAqipqbl93KOD6uQgu1PXEfqd32meBvjGNzYPSNyjz2NiYu4yPt78\nejJatVgKIETzkOYHUf/8z81TAN/xDnjmMxd+1itZJwpaG0wl87uSgEqB1ba13friUq1ELawtOs8o\nCAOOzRzjwOABgjCgO7/Bc0JFRGRLWE11u98A/s7d74xvj5jZy9z9z5d56Lbi8YGv4wu2LbrdwLtz\n0J2DgV5813CyA1SreDUefSoW8ZkZKE7DVAlPzafxXA5yURDlqfS95PUMw8zIkIn/jW4bRsYy9fvb\nbrVpgGZRWt3AAJx77speo1aD06eXDqgmJqKUwHvvjYKwZo4diyoGDgxEI1bJqFVyPT2KNf/+3t7W\nBFP/+I/wnvdEbdm7N6pe+Mxnzt2ffNeL/Zt8hvO3my28LLY9uS+TWbg9CeIymeiy2HVpme3WF89U\nZqJQcBEnZk9QC2tKtxMRkZZaTbrdr7r7u5Mb7j5hZr/KXIWlba9QLnD3ybujwCQ1haUh+PD0Va/f\n5+5YfCSw6PaMYzsMdhiE3VCrQjWIgoLiFMwWoVTCwwBzwCx6fPpAFhoOXKMgygCvT3jOkiWTyZDB\nyGWyZMiQtWx0f2pbNEl6LsiK/qUh8Eq2pQOxTLvTAHO5uSp7F120/P7XXNO8EuDQELz4xXOjU5OT\n0fX77ouuT08v/pzd3QuDquUCrMHBxhGim2+GP/7juVGuhx+Gt70tCtqSzy+9ftRK/g3DtT0u4Q6f\n+Qy8+90LA7eGv3NvLIoxv4jJ/Ou53NzfZbNgSyNnaduqL54oTdCTbV76G6JUO4jKf4ceKkgSEZGW\nWE2QlDEz83j4w8yygH6NUsYKY3Rlu5bMnT8jkgpuSRrf7AxUa9H2Wi3eHo9WJFWgHNxD3EJCqngY\n4jhVA89kCA3cDLcozgsz4JbBLXqwYalwKw7s0iNdqX0AMmbkLMdgvp+dXUP0ZnvoyXafmdGs+Rar\nBPgHf7B0MFepRCM/SQCVBFHN/j10KLp++vRcoDJfLhcFZknQ9J3vNE8DfPObo1GwdICRTs2bX5Ev\nWR+q2f6L7bfYfLibb4a3vnXpwK2ZIIjedxhGjw2C6G8jDOdGzpLXSwKs5DpEwdL895cufpIOstJB\n1fwRsiWue2p/t9T15UaCl9me+ejHyL3+DVwFiyxetmrbpi8OPWSyNMmO7h2L7jN6OjrBkaTbKUgS\nEZFWWE2Q9FngE2b2XqLjiV8D/rEtrepA5VqZidIEwz3DG92UxjksEI2oNJMctMYXC0PMQzKhz22v\nVuN0sBrUAgiDKOAKQ6hU4wPaJNBK0gdT6VXxiBaZ7FzalxmOEbhTKJ3m1OwpMCObyTLcNcRw1yB9\nuV56sz2bMwUw0dW1uqIVEH1up083BlDzA6zk+vwAKXH6dDTC1G5JYJK+TE4uDPJKpai0/G23za0/\n1dcH/f2Na1Il2+bf7u9fdJFfdyf0kCCsEYYBQa1EWJwlCKqEYUC1VqEaVKgGVXr+6TZ2/eVHyZ84\nSXXPLkZ/+blM/NgTwZ3Q5kbGwrknJ7S563GEn2wgyfGyVHqhm9Vvu0WjpvU0RIBMEnRF9+/63Je4\n4G3vJVOqtOIbSWybvrhYLRJ6uGQ/MDYdFYLZP7ifSq2i8t8iItISqwmSfg94OdFK7wZ8DvhAOxrV\niSZKE2duXk+rtGK+iPuCYIswbNyeHsGK599YrUYuCMh5jn6yEISElRrTs8c4VXsA4nlTw/kBhvM7\n6M/10mN5MunJ2/WgrEmaV7Pb81PH0qMJP/qjUeW99PybUmnuADj5rNb7/SbrRw0Pw8GDS+7q1zwV\nG11YCTA4ey/Tn/wIFoRY/FlmghCrBfHtgEwtwMIAqtG26P7a3Chj+jtpdkmPRqb3/ehHmze2XI5G\nvmZn5y6LjZg1e6/dXYS9vYR9PQS9PQQ93QS93dR6uwl7ewh6uwl7ewl6ewh7e+L9uvHeXsLeXga/\ndYi9f/v3ZCpRJcSu46c4710fpKdcY/opjwd3LPQoHTT06G/BicY24/vi4VSI7zdP3w6i/cOwfn/y\nd27J37sTnWzwuX32vuuvyLY2QIJt1BdPV6aXDXqOFo4y3DNMX76PSlDRQrIiItISq6luFwLvBd5r\nZjuBc9x9S6/NsVLuzlhhjP6u/o1uyplntnDkao0yQF98wZ0wDJitlhgPyuAh5s5Qdy87e3ZGI025\nHjKkAqDkstLb9YPbeYFeKpirBwiVSvRvGDbOtUl/DokkMEsHVunr824HYUAlrFIOK8zWikzXZinU\nZhj61edwwdv+gmx57iA76O7ivlc8l3E7BXnDcyHWY/URkLkyHTmS/95RTlZ0JZlDlp53liEaxcuQ\nrd+fnnuWsQzZTIYMGYa+cBvZsYcXfHfBvrM59vd/TTWsUQlrBF6lWpwlnJ0hnJkmWyyRnS2RKZUb\nrmfi67lke7EcX0rkiiW6p6axYonMbIlMsUimuMjoWrO/p3KFs9/1AXjX1ooftlNffKp4ip7c4vOR\nYG6NJIj64qwpSBIRkfVbTXW7LwA/HT/mG8AJM/uiu1/fprZ1jEKlQCWobM8gqV3MyGRz9GYH6GUA\niA6ASrUS980cjfeBHV07GOkdob+rn95cb/vPIi82crbU6Fl88VqNSqVIuVqkXC1xunya6eoMpbBK\nEt5kLUPecvRl8oRPeTLHq8buD3yE3IlT1Pbs4uSv/ALhU5/CcDVJ68ourEIXf37NKtY5TojXBz6c\nKJ2tFgR4fbtH89Pi+6N9onS0XS9/bvPA7eXPY7J4PA6wMmQtQ6anl1xvH9ndZy/4GAPWuPppGGLl\nCpnZIpliEYuDp3N/5XeaFkBz4OE3vToVnCafw9z1dCrdcvt5+v441a4+fykVACfzmw5c/0ZypybW\n8k4XtV364lpYo1AuMNI7suR+o4VRDg4frN/WSJKIiLTCatLthtz9tJn9CvAhd3+jmd3ZroZ1kmMz\nxzRZ+AwwM3rzvfTme4EoaCoHZY5MHalPlt/RHQdN+X768n2tP2Ba4chZNahSCSqUgzLT5WkKlVlm\nqjNRtUHLA3nymZ10ZfKMWHZhkBWnbBUOHqTw0hcuDMZgwb4NI2P43LakMEI87yw7f1QteV/Rh9p4\ne26H6Cl+9CkLA7eXvYDwKU9iRzEkKqsYNKYmpkuQNy0pHj//SlIZMxm8N07JY+7guXb2WeQfPr5g\n99rZZ1H4yWuXf96VSD5XZ/GRyuR6nGp44td+ib1/+h4y5Zam3G2Lvni2OrvsPu7OaGGUJ577xPo2\njSSJiEgrrCZIypnZPuB5wOva1J6OUwkqjM+Ob46CDduMmdGT66mn47g7laDCA1MP1IOmga4BRnpG\nGOwepDffSy6zmj/55QVhUA+GZiuzFCoFpivTBGEAFrUpn83Tle1iqHto8TlrLUhXXJP0wX6z4KnJ\nfYWLLqTwihfPBQvp4My9sZLdgtG2OKBLRtqaBX9LBUvz55zF207+8s+z94a/aAhGwu4uTv7yz0eF\nLpZ73uS5l5JOk5xfTj9jUcGS+j7R7cILfg527GDXu/4CxhYGcWu0Lfri0+XTy57kmCpPMVudZf/A\n/vo2jSSJiEgrlhK3rAAAIABJREFUrOaI8c1EVZW+5O5fNbMLge+3p1mdY6I4ES3K2kkFG7YoM6M7\n1013rru+rRJUOFo4Sng6qpDVm+tlV+8uBroH6M31ks/mV/TcSQBWDsqUa+U4VW6aUnVujkw2kyWf\nybdnBKtd5qfpbaT5AVl6TaeGbfNGc8KQwkvPg1272H3De8iNHae27yxOXv9rFJ79E42pcPUL1Eev\nmi2cOy99bj2f0UeeNMQ7s1nG3rnOz2fOtuiLVzofCaLKdu5za72JiIis12oKN9wI3Ji6fRj4L8lt\nM3utu5+BusSbR1KwYcPXRZJFdWW7GlIhK0GF0elRwkKIu9Ob72Vn704Guwbpy/eRz+abpMoVUqly\n0cFyPhONDi03X0JWYZ0BW+ElL6Dwkhe0sEHrd/Ohm3n9ba+nVFt5wYnlbIe+uBJUKFVLK5qPBFGQ\nFLjWSBIRkdZpZe7Rc4GO/mFerenKNOWgTF+XgqRO0SxoOjZ9jKNhVAwiY5koVW81qXKyKdx86GZu\n+PINjBXG2De4j+sffz3XXbLMWlerVA2qzFZn65eZ6szcv5WF2z/67Y+2NEBaoY7vi1cyHwnmgqQD\nOw4QerjikWEREZHltDJI2nZHkMdnjutHucPND5pCD5Wu04Hmj9iMFkZ5/W2vZ6Y6w5PPe3LTwKZ+\nuzLTdHvD/nHhjWpYXXGburPdlINyu97yUjq+L54sTa6obx0tjNKT62GkZ4RSrUR3vnvZx4iIiKxE\nK4OkZWY9by3VoMqp4imGuoc2uinSQgqQNp9yrcxkaZKJ0kR0KU7Ub0+WJpkoTvC5ez+3ICAp1Uq8\n8QtvXNFr9OZ66cv31S/9Xf0Mdg9y9sDZDdvr98fVE5N9529PioRc8+Fr6qMdZ1DH98XjxfFl5yNB\nFCTtG9iHmSndTkREWkojSWs0WZrE8U2dgnUm0o9k+1nP31WpVqoHNosGPsVUAFSaWDL1KqleuNSI\nzVuf9tZ6AJMOaJJLO9fXuv7x17d8TtIKbN5OaQVKtRLVoMpA18Cy+44WRjkweACIRoEVJImISKu0\nMki6cfldtgZ3Z3R6lP785l08drH0I0CBkqxZs7+r133+dRw6dYjLdl/WMLqTDnSSbcVacdHnHuwa\nZKR3hJGeEXb37ebinRcz3DNc35ZcH+4ZZqRnhKGeofpB8WIjNvsH9/Ocy5/Tng9jBZL/a+/8j3cy\nxtiZetmO7otnKjMrDvNGC6NcuvtSICrHryBJRERaZUVBkpk9AzgHuNXd709tf6m7fxDA3f9okcc+\nE/j/gCzwAXd/2yL7PYfox/2x7n7Hat7EmTZTnVlR5aWNUg2qvOPf37Hg7HWpVuId//4OnvGIZ+hg\nokO0YzSwFtaYrkw3XArlaH2nZJ2n+vbkdnma6eo0h04eIvCg4fnKQZn3f/39DduGuofqwcxZfWdx\nya5LmgY6yfWh7qF1ze9rNmLTk+vh+sdfv+bnbJXrLrmOay+8litec8W31/tca+2LO6kfHi+O051d\nfm5RqVbiVPEU+wejNZIM65zS+yIisuktGySZ2R8BTwK+Dvy+mb3L3f8svvuVwAeXeGwWeDfwdOAh\n4KtmdpO73zVvv0HgN4GvrOldnGEnZk4sOKBrV2pbJagwWZpsena+IWUpdX26Mr3o8x2bOcaj3/No\n+vJ99YPToZ6h+vXhnuG5672N23Z072hJcKU0wJVZbDRwqjTFE859Qj2AaQhklgh0CuVCvTjBcrKW\nZbBrkIHuAQa6BhjsGmRv/17uOnHXoo+55Rduif52eoZavmjvcpK/n638d7XWvriT+mF3Z7I0yWD3\n4LL7pst/A2DR362IiEgrrORI5jrgSnevmdmbgI+Y2YXu/tssnxTxOOCeeB0PzOxjwLOB+Uda/wP4\nE+DVq2n8RqiFNU7Mnmgo2LDS1LYk4FlpsDNZmlwy4OnL9zWcnT84fLB+/cPf+DBT5akFjxnqHuIl\nV7yEqdIUk6VJpsrRv4dOHmKqPMVUaWrBSEGz1xzqGaoHUEM9Qwx3D89dn7dtR/eOelCpNMCluTtH\nC0f57snv8odf/MOmo4H/41//x5LP0ZfviwKcOLjZ0b2D/YP769uSS32f7sEF23pyPU3n2y2V1nbR\nzovW9+bX6bpLrtvqf0Nr7Ys7ph8u1oorrjA5VojSF5M5STgaSRIRkZZZSZCUc/cagLtPmtl1wPvM\n7EZguWGFA8CDqdsPAT+c3sHMrgTOdfdPm9miP85m9nLg5QDnnXfeCprdHpPFSXAaDiBv+PINTQ9m\nX/f51/FX3/yremA0U51Z9Hn78/0N8y8ODh9cMBejfj1OU1pqVOe8Hec1TT/6g6f8wZIHku7OTHWG\nidIEU6WpejA1WZ6cC6xKU/Xg6rsnv7ui4Cp5f8dnji8oo1yqlfjTf//TrX6Au0AlqHB44jB3n7ib\nu0/eXf+3UCks+9gbfvyGKLDpHmAgPxfo9Of723qguJnT2raBtfbFLeuH433b1hcXygVshROSkmB9\n3+C+uGEaSRIRkdZZSZB0r5ldQ3Qm8kF3D4CXmdlbSK3yvohmv3b18rRmlgH+J/CS5Rrh7u8D3gdw\n9dVXb1iJ29Hp0QWLxyZnNOcrB2VGeka4cOTCJYOd4Z7hls8RWmv6kZnVRxXO3XHuil/P3ZmuTC8I\npibLk3OBVWmKfzj0D00f//DMw/zwB36YC0cu5KKRi7ho5CIuHLmQC3deyIHBAx1fmrtQLvDdk9+N\ngqGTd/Pdk9/l+6e+Xw8Ye3I9XLLrEp518bO4fM/lXLb7Mn7rH3+LsemFf1v7B/fzk4/8yTP9FoDt\nkda2ia21L25ZPwzt7YvHi+P05Jcv/Q1wtHCUjGXY2783bphGkkREpHVWEiQ9l+hH9l+Bq5KN7v56\nM3vPMo99CEgfaZ8DpHN1BoEfAL4Qj8ycDdxkZj+9GYs3zFRmKFaLCwo27Bvct2gK0gd++gNnqnkL\nnMn0IzNjsHuQwe7BJYOr20dvb/pZ7ejewTMuegaHJw5z6323cuNdcwW6urPdXDBywVzgFAdSF4xc\nsOkKULg7x2aOcdeJu6Jg6EQUGD14eu5E/s7enVy++3JefMWLuWz3ZVy25zIODh1ccID3O0/4nU05\narMN0trWLAgDAg/q/4YeEoQBtTAaAFrn06+1L+6IfjgIA06XTzPcM7yi/ccKY+zt31tP5XVzjSSJ\niEjLLBskuXsRwMy+bGaPdfevpu47uszDvwpcbGYXAEeB5wO/kHr8FLA7uW1mXwBevRkDJIATsyea\nTki//vHX89pbX9uQRrYZDmY3o8XStd7wlDc0HHhPFCc4PHmYw+OHuXfiXu6duJdvHvsmt3z/Fjw+\n1sxYhnN2nLMgeLpo50Xs6N7R9vdSC2vcN3FfQ6rc3SfvZrI0Wd/n4NBBHnXWo3jO5c+pB0R7+vas\naH0tjdpsvCTICT2kFtai2x7gHq+R5oBRv53P5Mln8vTme+nOdtOV7aIr2xUFwDWqy77gEtbRF3dE\nP5wUFFnp2nOjhdF60YbQQ7JkN/W6dSIi0llWU4LqGuAVZnYEmCE6o+nu/pjFHhBPMH4l8Fmi0rMf\ndPfvmNmbgTvc/aZ1tP2MqoU1js8cb3rwfd0l13Hz927mi0e+iGE6mF3CSg/8R3pHuKr3Kq7ad1XD\n9mK1yP2T93N4Yi54Ojx+mC898KWGIHV33+560JQOnvb27216ILVcxb2ZygyHTh2qjw7ddfIuvnfq\ne1SCCgBd2S4u3nkxT7/w6Vy2+zIu3XMpl+y6ZEULYi73eenvqHXcvT7CUw964iAIqAc+joNBznLk\ns3m6Ml305/vpzkWBTy6TI5vJRv9almwmS9aWPUhvVWraqvriTumHC+XCqtJqjxaOcuW+K4FoFCqf\nW3sJeRERkflWEyT9xFpewN1vAW6Zt+0Ni+z71LW8xpkwVZrC3Rf9Ec9lcly882I+/QufPsMt6zzr\nOfDvzfdy2Z5oRCYtCAMeOv1QFDTFAdTh8cN8+nufbiiE0JfvWzDv6cjUEf7s9j9rqLj3+5//fW49\nfCsY3H3ybo5MHqmPYA13D3Ppnkt54aNfGLVl92VcMHzButb5kbVbLMUNorVzohAiCnwylqEr20U+\nm2ega6A+2pPP5slath78JIHPJp0Lt+q+uBP64VPFU/Tme1e0bxAGHJs5Vq9sF3pIV2Zzpd6KiEhn\nW3GQ5O5H2tmQzW5seoy+fN+i9z8w9QDnDW1c1b3tLpvJcv7w+Zw/fD5Pu+Bp9e3uzsnZk/VRp/sm\n7uPeiXv58kNf5lOHPrXo81WCCp+59zOcs+McLtt9Gdc98rp6QYWzB85WWk8bJUFOEvisJ8Vt/kjP\nVpjYvxX74mpQZbY6u+IFuk/MnqAW1urpdoEH9GZXFmCJiIisxJld8bFDzVZnmanMLPoDHnrIA1MP\n8OTzn3yGWybLMTP29O9hT/8eHn/O4xvum65Mc3jiMM+98bnNH4tx6y/deiaauaUlKW7zR3pCD+sj\nPe5xJtq8FLfurrmgJ5fJLRjpWUGKm3SAlSxwnHa0EE3BSsp/hx6Sz2gkV0REWkdB0gqcnDm55Bno\nY9PHKAdlzh86/wy2StZroGuAx+x9DPsH9zetuFdff0UWcHeqYXXBiE/DnJ5YkuLWle2iL9tXv57P\n5heM9OQyOQU929BkaXJV6aqjp6P/rw3pdpus0qWIiHQ2BUnLCMKAh2ceZrBrcNF97p+6H4DzhxUk\ndSItkNqcu1MLa1TDKtWgirvjeD2I6cv10ZefC3rSBQ2SwCeXyW3WeT2yiYwXx+nJrWx9JKC+flg9\n3S4MFCSJiEhLKUhaxunyadx9yZGkByYfANBIUofa7qW2a2GNalCNRoY8ICrsZrg5vbleBroG6M/3\n05PraQiGNOIjrVCulakEFfq7+lf8mKOFowz3DNfniRq2JeabiYjI5qEgaRljhbFlKy7dP3U/Xdku\nzh44+wy1Slptq5faroW1ejAUL2yKmeE4Pdke+vJ99Us+m4/S4TJ5BULSdjPVmVU/Jr1GEgCGFpIV\nEZGWUpC0hGK1yOnyaXb27Vxyv6SyndKKZCMFYVBPj6sFtYaCCF3ZLvryfYz0jNDf1U8+k6/PC9Lf\nrWyk8eL4qlPlRgujHBw+OLfB0UiSiIi0lIKkJZwqnlrRD++RySNKtZMzIlkEtRJUohGhuEiCmZG1\nLP35fnZ076A/309Xrqs+IqQDSNmM3J3J0uSqFl12d0YLozzx3CfObdRIkoiItJiCpEUEYcDD0w8v\n++Ot8t/SDkn1uHKtTBAGUSCEkbEMfV197OzdSX++n+5cd31USIGQdJpirUgQBqsazZwqTzFbnWX/\nQCrdTiNJIiLSYgqSFlGoFAjCYNkf3s1W/js5uE7mniRr0aRLMqfLLScVyGTjJN9ZJahQC2rRd2XQ\nn+vnrP6zGOgaoDvXXS+YILJVzFTWNh8JaJiT5OYaSRIRkZbSEdcixgpjKypJuxHlv5crzdyb641S\nrrqiimTJIovJ5P1SrUSpVqIclCnXyhTCAqkYCogm9afXsNEk/tZYKiDa07eHga4BenI9dOe6NVdI\ntrzx4viyhXHmmx8khR6SM1VbFBGR1lKQ1ESpVmKqPMXO3qULNkB7y38no0HzSzNj0To+80sz57P5\nNQUzSdCVvlSCSj2QKtVKUSn0eZGUuzeMRiUBlUSaBURmRl+uj929uxnsHlRAJNtWEAZMliYZ7hle\n1eOSIOnAjgP151nNQrQiIiIroSCpifHZ8RWnbqy3/He6LHMtrM2lxsWBUF++j/58P7353raVZjaz\nKMBa5kAjqZ6WvqRHpUq1EpWwEgVyMcfJkGkIpLbiGjtLjRApIBJZqFgrAqy6LxgtjNKT62GkZwSI\nRpK6MlpIVkREWktB0jyhh4xOj654YcOVlP8OwqBhnhDEa9S4053tpq8rtUbNJi7NnM1EI0XddC+6\nz0pGpWbLs3OjUk5DqeqMRQFVxjL1S9ai25slsEoHRNWgGm1UQCSyKoVyYU3/P0YLo+wb2FfvDwIP\n6Mv2tbp5IiKyzSlImqdQjgo2rHSCfLr8d+ghs9XZJdeo6cv31YOgrmzXljuIXu2oVOABQRgQeEDo\nIdUgCj6SEtfVoEopKFEJKvXnT5e9Tq6nA6skqEoCrvVoFhDNT5nrznXTk+vZct+lSDudmj216vlI\nEAVJBwYP1G+HHq56nSUREZHlKEia5+Hph+nOLT5SklYv/31eVP57tjobHTzv2K01apaRjEqtRhBG\ngdT8wCoIgwWBVSWMRq9qYa15YGVzJbWTwCppT8MIEdCf71dAJNJC1aDKTHWGkd6RVT92tDDKpbsv\nrd/WnCQREWkHBUkp5VqZieIEO/uWL9gAqfLfcWW7IAwY6R1hd//udjZz28pmsmTJkmflB0Tu3hBY\npa8nAVV9pCiMKgUqIBJpr9nq7JoeV6qVOFU81VD+O/SwXsFTRESkVRQkpYwXx1d1QHxk6ghAQ7qd\nzmhuLmYWjRKRBQ3oiWwKU6WpNa35NVYYAxrXSAItJCsiIq2nU+Sx0EPGCmMMdA+s+DFHJuMgKbVG\nkhb7FBFZ2nhxfEXr0M1XL/+dmpMEaCFZERFpOQVJsenKNJWwsqog58jUkYby38mohYiINFeulSkH\n5TWNuidB0r7BfQ3bNZIkIiKtpiApdmz6GN3ZlRVsSByZOtJQ/tvd9WMtIrKEtc5HAjhaOErGMuzt\n39uwXSenRESk1RQkEVUzGy+O05df3VobD0xGaySlKd1ORGRxE8WJNZfsHiuMsbd/b8MolGE6OSUi\nIi2nIInoRxtWt/J76CFHpo5wcOjg3EbTGU0RkcW4OxOliTXNR4J4Idl5qXZurn5XRERabtsHSe7O\naGGUga6VF2yAufLf5w1HI0mhh+Qst6pAS0RkO0nWLlvryM/RwtEF5b/V74qISDts+yBpujJNubb6\nScRJ+e9kJKkW1lT+W0RkCTOVmTU/NggDjs0ca6hsp4VkRUSkXdoeJJnZM83skJndY2avaXL/9WZ2\nl5ndaWa3mtn5zZ6nXY7NHKMrt/r8+KT8dzInKfRwzSkkIiLttFn64VPFU2vuJ0/MnqAW1haMJHVl\n1ja/SUREZCltDZLMLAu8G/gJ4HLgBWZ2+bzd/hO42t0fA3wS+JN2timtElQ4NXuK/nz/qh+blP9O\n8uODMNCq7yKy6WyWfjj0kKny1JqDpKOFo0Bj+e/ANZIkIiLt0e6RpMcB97j7YXevAB8Dnp3ewd1v\nc/ekJuyXgXPa3Ka6ydIk2OoKNiSOTB3h3B3n1st/Bx6suWKTiEgbbYp+eLY6i7uvef7Q6OmFC8mG\nHqrfFRGRtmh3kHQAeDB1+6F422JeBnym2R1m9nIzu8PM7jhx4sS6G+bujJ4eXdMoEkTlv88fnstI\nCcJA6XYishm1rB+GtffF05XpdRVYGJseA2DfQGokKdTJKRERaY92B0nNfhG96Y5mvwhcDbyj2f3u\n/j53v9rdr96zZ8+6GzZTnaEUlNb0A9us/LfW6hCRTapl/TCsvS8+NXuK3lzvivef72jhKMPdw/R3\nzZ3YCj1Uup2IiLRFu1c+fQg4N3X7HGB0/k5mdi3wOuBH3b3c5jYBcHz6+JrPQB6fOd5Q/hvA0Vod\nIrIpbXg/XAtrzFRnGO4ZXvNzjBZG2b9jf8M2M1O/KyIibdHukaSvAheb2QVm1gU8H7gpvYOZXQn8\nBfDT7n68ze0BoBpUOVk8ueZUu/sn7wdoHEkyI5dpd8wpIrJqG94Pz1Znl99pGaOF0YbKdgA4GsEX\nEZG2aGuQ5O414JXAZ4G7gU+4+3fM7M1m9tPxbu8ABoAbzewbZnbTIk/XMpOlyXVNIH5g6gFgrvw3\noB9rEdmUNkM/fLp8el0jPsmi3wuCJEMjSSIi0hZtH/pw91uAW+Zte0Pq+rXtbsO812Z0erQhr321\n7p+8v6H8NyjdTkQ2r43uh9ezPhLAVHmK2eos+wc0kiQiImdG2xeT3Wxmq7MUK8V1VUR6YOqBhvLf\n7k7GMvqxFhGZpxJUKFVL6yqwMFqIplDNH0lyvN4Pi4iItNK2+3U5PnN83dWQjkweaSz/rTWSRESa\natV8JFgYJCndTkRE2mVbBUm1sMaJ2RPrSrULPeSB0w9w/tD5DdtUhlZEZKHx2fF194/NgqQgDMhZ\nbl1rL4mIiCxmWwVJk8XJemrcWh2fOU6pVmoYSaqFNY0kiYjM4+5MlCbWtT4SREFST66Hnb0769sC\nD3RySkRE2mZbBUlj02PrGkWCKNUOWDCS1J3tXtfziohsNaVaiVpYW/d8zdHCKPsG9jWMGrk7XRmd\nnBIRkfbYNkHSTGWGmerMukd8jkwtDJKCUHOSRETmm6nMQAuy4UYLoxwYPNCwTSNJIiLSTtsmSDo5\ne5J8Zv0/qPdP3k8+k+fsgbPr2zQnSURkoYnSREtG2UcLow1LLkDU7+rklIiItMu2CJKCMODYzLF1\np9pBVP77vKHzGtJHDCOXafuSUyIiHSP0kMnS5LrWR4IoZe9U8dSCynYawRcRkXbaFkHSZGn9BRsS\nRyaPcN7QeY0bVYZWRKRBsVpsSb87VhgDFpb/1gi+iIi007YIksamx+jL9637eZLy3weHDzZsd3ct\nJCsikjJdmW5Jee7F1kgyM52cEhGRttnyQdJsdZaZygzdufXnxSflv+ePJCndTkSk0XhxfN2pdrDE\nQrKOTk6JiEjbbPkg6dTsqZb9kCblvxeMJJnrjKaISKwW1jhdPt2SOUNHC0fJWIa9/Xsb71Cas4iI\ntNGWDpKCMODh6Yfpz6+/YAPMlf9OjySFHmrVdxGRlGK1CNCSfnGsMMbe/r0L5x9pJElERNpoSwdJ\np8unCT1s3UjS1BHymTz7BuZK0dbCmhaSFRFJmSpPtazfbVb+G9BIkoiItNWWDpLGCmP05ntb9nxH\nJo9w7tC5DT/+oYd05VSGVkQkcap4qiXzkSBKt1swHwlaVrFURESkmS37C1OsFilUCi37oYZoJOn8\nofMbtgVh0JJFakVEtoJKUKFULbVkPlKyxt2BwQMLtndlu5TmLCIibbNlg6RTxVMtTcUIPeSBqYXl\nvwMPlG4nIhKbrc627LlOzJ6gFtYWpNsFrpNTIiLSXlsySAo9jAo2dLWmYAPAiZkTTct/B2HQkvLi\nIiJbwWRpsmWLvB4tHAW0kKyIiJx5WzJIOl0+TRAGLa18dP/k/cDC8t+GqcKSiEisVesjAYyejtZI\napZup5EkERFppy0ZJD08/XBL5yIBPDD1AMCCkSRHaySJiACUaiVqYa1li2uPTY8BNFQUBRXMERGR\n9ttyQVKpVmKqNNXSqnYA90/dv6D8N0TrgLTqgEBEpJPNVmdxvGXPd7RwlOHu4QWp04EHdGUUJImI\nSPtsuSBpfHa8LWVhm5X/BrSgoYhIbLw43tJCNqOFUfbvaF7+O5fVySkREWmfLRUkhR4yNj3W0oIN\niWblv0HpdiIiEAUuE8WJlqY6jxXGmq6RBFpIVkRE2mtLBUmFcqGl+fCJpPz3/CApWcxQI0kist0V\na0VCD1s2ku/uHC0cXZDinFC/KyIi7bSlgqRj08faUo47Kf99/vC8hWQ9aMmCiSIina5QLmC0bnHX\nqfIUs9XZBZXtEhpJEhGRdmp7kGRmzzSzQ2Z2j5m9psn93Wb28fj+r5jZwbW8TrlWZqI0QV++b71N\nXiAp/z1/JElrdYhIJzgT/fB4cZyefOtS7UYLUfnvZul2WnpBRETara1BkpllgXcDPwFcDrzAzC6f\nt9vLgAl3fwTwP4G3r+W1xovjLT2LmZaU/54/klQLaxpJEpFN7Uz0w0EYcLp8uuVFG6B5kIRpJElE\nRNqr3SNJjwPucffD7l4BPgY8e94+zwY+HF//JPBjZraqaMfdeXj64bYUbIDFy3+HHrb0oEBEpA3a\n3g/PVmeBaEmEVlksSHJ33F0jSSIi0lbtDpIOAA+mbj8Ub2u6j7vXgClg12pepFApUAkqbUt9e2Dy\ngablv4NQc5JEZNNrez9cKBdavvTCaGGUnlwPO3t3NmwPPVS/KyIibdfuIKnZacX5Kw2uZB/M7OVm\ndoeZ3XHixImG+47NHGvrj+b9U/c3Lf+tOUki0gFa1g9D8774VPFUyxfwHi2Msm9g34LRqcAD8hn1\nuyIi0l7tDpIeAs5N3T4HGF1sHzPLAUPA+Pwncvf3ufvV7n71nj176tsrQYWJ2fYUbIhft2n5b4gm\nD7e63LiISIu1rB+GhX1xNahSrBZbfqJqtDDadD5S6CFdOY0kiYhIe7U7SPoqcLGZXWBmXcDzgZvm\n7XMT8OL4+nOAz7t70zOYzUwUJ8BamwufdnzmOKVaifOGz1t4pyYPi8jm19Z+eLY6izcfdFqXxYKk\nINRIkoiItF9bh0HcvWZmrwQ+C2SBD7r7d8zszcAd7n4T8JfA35jZPURnLp+/iudnrDBGf749BRsA\njkwdAeDg0MGmr6/JwyKymbW7H54sTbY87bhUK3GqeGrxkSTNSRIRkTZre66Yu98C3DJv2xtS10vA\nc9fy3NOVaUq1En1d7Um1AzgyGQVJzUaSlG4nIp2gnf3weHGcnlzr1kcCGCuMAc3Lf2sRbxERORPa\nvphsOx2fOd723PQjU0fIZ/LsH1j4Y+3mSrcTkW3L3akElZafLFpqjSTHdXJKRETarmODpGpQ5eTs\nybam2kE0knTOjnOalv/OWa5tc6FERDa7wIO2LOK9VJBkbkpzFhGRtuvYIGmi1N6CDYkjU0c4OHxw\nwfbAAy0kKyLbWhAGbVkGYXR6lIxl2Nu/d+GdRsvXZBIREZnPVlFIbtMwswJ5HiDKvNiYN2BkcEJq\nlNfw6N3AyVY36Qzr9Peg9m+8Tn8Pq23/+e6+Z/ndOoeZFYBDG92Oddhuf4ObUae/B7V/423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mb2+3FOfdPLEg+9c72vLSKSor53ZX3vUr4DPMbM0p/ZY+LtItKhFCTJZjEIlIFTQB/RCEmdmb0I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\niIiIhn8ASf4QE31s0K4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10578ba90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 根据不同的训练集大小，和最大深度，生成学习曲线\n",
    "vs.ModelLearning(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 4 - 学习曲线\n",
    "*选择上述图像中的其中一个，并给出其最大深度。随着训练数据量的增加，训练集曲线的评分有怎样的变化？验证集曲线呢？如果有更多的训练数据，是否能有效提升模型的表现呢？*\n",
    "\n",
    "**提示：**学习曲线的评分是否最终会收敛到特定的值？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 4 - 回答:\n",
    "\n",
    "最大深度为1时，随着训练数据的增加，训练集和验证集两条曲线的评分趋向于稳定在大约0.4多一点的位置。再增加训练数据不能再有效提升模型的表现。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 复杂度曲线\n",
    "下列代码内的区域会输出一幅图像，它展示了一个已经经过训练和验证的决策树模型在不同最大深度条件下的表现。这个图形将包含两条曲线，一个是训练集的变化，一个是验证集的变化。跟**学习曲线**相似，阴影区域代表该曲线的不确定性，模型训练和测试部分的评分都用的 `performance_metric` 函数。\n",
    "\n",
    "运行下方区域中的代码，并利用输出的图形并回答下面的两个问题。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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G2PKt0+g+/Qv4s3PsjCw+nw284uL4sXaj7UcLRUM09zTHg2uoS1eoa9B9c3w5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\nscRnjDEmqPw/S2X4HSOEXM4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aa59110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 根据不同的最大深度参数，生成复杂度曲线\n",
    "vs.ModelComplexity(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 5 - 偏差（bias）与方差（variance）之间的权衡取舍\n",
    "*当模型以最大深度 1训练时，模型的预测是出现很大的偏差还是出现了很大的方差？当模型以最大深度10训练时，情形又如何呢？图形中的哪些特征能够支持你的结论？*\n",
    "  \n",
    "**提示：** 你如何得知模型是否出现了偏差很大或者方差很大的问题？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 5 - 回答:\n",
    "\n",
    "图形中，模型以最大深度为1训练时，红点和绿点在得分轴上坐标都处于0.4和0.5之间。说明训练得分和验证得分都较低，此时模型的预测出现了较大的偏差，属于欠拟合。\n",
    "\n",
    "图形中，模型以最大深度为10训练时，红点和绿点在得分轴上坐标之间的差距逐渐增加到了0.2多。说明训练得分很高但是验证得分较低，两个得分相差较大，此时模型的预测出现了较大的方差。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 6- 最优模型的猜测\n",
    "*结合问题 5 中的图，你认为最大深度是多少的模型能够最好地对未见过的数据进行预测？你得出这个答案的依据是什么？*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 6 - 回答:\n",
    "\n",
    "预测：深度为3时，模型能够较好的对未见过的数据进行预测。因为在深度为3时，验证集的得分达到第二高的位置，而且验证集与训练集之间的得分差异最小。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第五步. 选择最优参数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 7- 网格搜索（Grid Search）\n",
    "*什么是网格搜索法？如何用它来优化模型？*\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 7 - 回答:\n",
    "\n",
    "网格搜索法是指定参数值的一种穷举搜索方法，通过将估计函数的参数通过交叉验证的方法进行优化来得到最优的学习算法。 即，将各个参数可能的取值进行排列组合，列出所有可能的组合结果生成“网格”。然后将各组合用于训练，并使用交叉验证对表现进行评估。选取交叉验证结果最好的一个模型作为最优模型。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 8 - 交叉验证\n",
    "- 什么是K折交叉验证法（k-fold cross-validation）？\n",
    "- [GridSearchCV](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html)是如何结合交叉验证来完成对最佳参数组合的选择的？\n",
    "- [GridSearchCV](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html)中的`'cv_results_'`属性能告诉我们什么？\n",
    "- 网格搜索时如果不使用交叉验证会有什么问题？交叉验证又是如何解决这个问题的？\n",
    "\n",
    "**提示：** 在下面 fit_model函数最后加入 `print pd.DataFrame(grid.cv_results_)` 可以帮你查看更多信息。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 8 - 回答：\n",
    "\n",
    "\n",
    "首先，K折交叉验证是将训练数据集随机分为K份，依次取第0份到第k-1份中的1份作为验证集，其余的K-1份作为训练集，重复K次“训练->验证”的过程。将K次的平均得分作为验证结果。之所以要选取平均得分作为最后的结果，是因为能避免样本数量非常小的情况下，某些异常值对逆推断结论进行严重干扰等问题。其实K折交叉验证并不限于(K-1):1，也可以做(K-2):2，或者(K-3):3等等。\n",
    "\n",
    "GridSearchCV实现了fit训练方法和score评分方法，同时根据传入的estimator参数类型的不同来实现“predict”, “predict_proba”, “decision_function”, “transform” and “inverse_transform”方法。根据给定的estimator自动进行交叉验证，通过调节每一个参数来跟踪评分结果，实际上，该过程代替了进行参数搜索时的for循环过程。\n",
    "\n",
    "GridSearchCV中的cvresults返回的是一个masked ndarrays组成的字典，可以转换为DataFrame类型。包含若干参数，如超参数字典params，如mean_fit_time, std_fit_time, mean_score_time和std_score_time等以秒为单位的值，如param_开头的参数及对应的masked array等。\n",
    "\n",
    "由于网格搜索仅仅依靠交叉验证来对各种穷举模型进行验证。如果不用交叉验证，网格搜索就得不到验证，有较大几率会出现过拟合的问题。使用交叉验证可降低出现过拟合的几率。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 4：训练最优模型\n",
    "在这个练习中，你将需要将所学到的内容整合，使用**决策树算法**训练一个模型。为了得出的是一个最优模型，你需要使用网格搜索法训练模型，以找到最佳的 `'max_depth'` 参数。你可以把`'max_depth'` 参数理解为决策树算法在做出预测前，允许其对数据提出问题的数量。决策树是**监督学习算法**中的一种。\n",
    "\n",
    "在下方 `fit_model` 函数中，你需要做的是：\n",
    "1. **定义 `'cross_validator'` 变量**: 使用 `sklearn.model_selection` 中的 [`KFold`](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.KFold.html) 创建一个交叉验证生成器对象;\n",
    "2. **定义 `'regressor'` 变量**: 使用  `sklearn.tree` 中的 [`DecisionTreeRegressor`](http://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeRegressor.html) 创建一个决策树的回归函数;\n",
    "3. **定义 `'params'` 变量**: 为 `'max_depth'` 参数创造一个字典，它的值是从1至10的数组;\n",
    "4. **定义 `'scoring_fnc'` 变量**: 使用 `sklearn.metrics` 中的 [`make_scorer`](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.make_scorer.html)  创建一个评分函数；\n",
    " 将 `‘performance_metric’` 作为参数传至这个函数中；\n",
    "5. **定义 `'grid'` 变量**: 使用 `sklearn.model_selection` 中的 [`GridSearchCV`](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html) 创建一个网格搜索对象；将变量`'regressor'`, `'params'`, `'scoring_fnc'`和 `'cross_validator'` 作为参数传至这个对象构造函数中；\n",
    "  \n",
    "如果你对python函数的默认参数定义和传递不熟悉，可以参考这个MIT课程的[视频](http://cn-static.udacity.com/mlnd/videos/MIT600XXT114-V004200_DTH.mp4)。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO 4\n",
    "\n",
    "#提示: 导入 'KFold' 'DecisionTreeRegressor' 'make_scorer' 'GridSearchCV' \n",
    "from sklearn.model_selection import KFold\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "from sklearn.metrics import make_scorer\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "\n",
    "\n",
    "def fit_model(X, y):\n",
    "    \"\"\" 基于输入数据 [X,y]，利于网格搜索找到最优的决策树模型\"\"\"\n",
    "    \n",
    "    cross_validator = KFold()\n",
    "    \n",
    "    regressor = DecisionTreeRegressor()\n",
    "\n",
    "    params = {'max_depth':range(1,11)}\n",
    "\n",
    "    scoring_fnc = make_scorer(performance_metric)\n",
    "\n",
    "    grid = GridSearchCV(regressor,params,scoring_fnc,cv=cross_validator)\n",
    "\n",
    "    # 基于输入数据 [X,y]，进行网格搜索\n",
    "    grid = grid.fit(X, y)\n",
    "\n",
    "    # 返回网格搜索后的最优模型\n",
    "    return grid.best_estimator_\n",
    "\n",
    "#GridSearchCV?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 4：训练最优模型 （可选）\n",
    "在这个练习中，你将需要将所学到的内容整合，使用**决策树算法**训练一个模型。为了得出的是一个最优模型，你需要使用网格搜索法训练模型，以找到最佳的 `'max_depth'` 参数。你可以把`'max_depth'` 参数理解为决策树算法在做出预测前，允许其对数据提出问题的数量。决策树是**监督学习算法**中的一种。\n",
    "\n",
    "在下方 `fit_model` 函数中，你需要做的是：\n",
    "\n",
    "- 遍历参数`‘max_depth’`的可选值 1～10，构造对应模型\n",
    "- 计算当前模型的交叉验证分数\n",
    "- 返回最优交叉验证分数对应的模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO 4 可选\n",
    "\n",
    "'''\n",
    "不允许使用 DecisionTreeRegressor 以外的任何 sklearn 库\n",
    "\n",
    "提示: 你可能需要实现下面的 cross_val_score 函数\n",
    "\n",
    "def cross_val_score(estimator, X, y, scoring = performance_metric, cv=3):\n",
    "    \"\"\" 返回每组交叉验证的模型分数的数组 \"\"\"\n",
    "    scores = [0,0,0]\n",
    "    return scores\n",
    "'''\n",
    "\n",
    "def fit_model2(X, y):\n",
    "    \"\"\" 基于输入数据 [X,y]，利于网格搜索找到最优的决策树模型\"\"\"\n",
    "    \n",
    "    #最优交叉验证分数对应的最优模型\n",
    "    best_estimator = None\n",
    "    \n",
    "    return best_estimator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 9 - 最优模型\n",
    "*最优模型的最大深度（maximum depth）是多少？此答案与你在**问题 6**所做的猜测是否相同？*\n",
    "\n",
    "运行下方区域内的代码，将决策树回归函数代入训练数据的集合，以得到最优化的模型。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter 'max_depth' is 4 for the optimal model.\n"
     ]
    }
   ],
   "source": [
    "# 基于训练数据，获得最优模型\n",
    "optimal_reg = fit_model(X_train, y_train)\n",
    "\n",
    "# 输出最优模型的 'max_depth' 参数\n",
    "print \"Parameter 'max_depth' is {} for the optimal model.\".format(optimal_reg.get_params()['max_depth'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 9 - 回答：\n",
    "\n",
    "最优模型的最大深度是4，与在问题6中所做的猜测3不同。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第六步. 做出预测\n",
    "当我们用数据训练出一个模型，它现在就可用于对新的数据进行预测。在决策树回归函数中，模型已经学会对新输入的数据*提问*，并返回对**目标变量**的预测值。你可以用这个预测来获取数据未知目标变量的信息，这些数据必须是不包含在训练数据之内的。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 10 - 预测销售价格\n",
    "想像你是一个在波士顿地区的房屋经纪人，并期待使用此模型以帮助你的客户评估他们想出售的房屋。你已经从你的三个客户收集到以下的资讯:\n",
    "\n",
    "| 特征 | 客戶 1 | 客戶 2 | 客戶 3 |\n",
    "| :---: | :---: | :---: | :---: |\n",
    "| 房屋内房间总数 | 5 间房间 | 4 间房间 | 8 间房间 |\n",
    "| 社区贫困指数（％被认为是贫困阶层） | 17% | 32% | 3% |\n",
    "| 邻近学校的学生-老师比例 | 15：1 | 22：1 | 12：1 |\n",
    "\n",
    "*你会建议每位客户的房屋销售的价格为多少？从房屋特征的数值判断，这样的价格合理吗？为什么？* \n",
    "\n",
    "**提示：**用你在**分析数据**部分计算出来的统计信息来帮助你证明你的答案。\n",
    "\n",
    "运行下列的代码区域，使用你优化的模型来为每位客户的房屋价值做出预测。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted selling price for Client 1's home: $406,420.00\n",
      "Predicted selling price for Client 2's home: $222,770.27\n",
      "Predicted selling price for Client 3's home: $943,854.55\n"
     ]
    }
   ],
   "source": [
    "# 生成三个客户的数据\n",
    "client_data = [[5, 17, 15], # 客户 1\n",
    "               [4, 32, 22], # 客户 2\n",
    "               [8, 3, 12]]  # 客户 3\n",
    "\n",
    "# 进行预测\n",
    "predicted_price = optimal_reg.predict(client_data)\n",
    "for i, price in enumerate(predicted_price):\n",
    "    print \"Predicted selling price for Client {}'s home: ${:,.2f}\".format(i+1, price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 10 - 回答：\n",
    "\n",
    "为第一位、第二位、第三位客户预测的价格分别是\\$406,420.00，\\$222,770.27，\\$943,854.55。从房屋特征的数值判断是合理的。第三位客户房屋内房间数8间最多，总价理应高一些，并且该社区贫困指数很低，意味着大家消费能力不低，价格高点可接受，两方面综合考虑，第三位房屋价格自然应当最高。第二位客户的房屋前两个特征情况正好与第三位相反，理应最低。第一位客户前两个房屋特征情况处于两者之间，所以房屋价格也应当处于两者之间。因此这些预测价格是合理的。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 5\n",
    "你刚刚预测了三个客户的房子的售价。在这个练习中，你将用你的最优模型在整个测试数据上进行预测, 并计算相对于目标变量的决定系数 R<sup>2</sup>的值**。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal model has R^2 score 0.80 on test data\n"
     ]
    }
   ],
   "source": [
    "#TODO 5\n",
    "\n",
    "# 提示：你可能需要用到 X_test, y_test, optimal_reg, performance_metric\n",
    "# 提示：你可能需要参考问题10的代码进行预测\n",
    "# 提示：你可能需要参考问题3的代码来计算R^2的值\n",
    "predicted_price=optimal_reg.predict(X_test)\n",
    "#print predicted_price\n",
    "r2 = performance_metric(y_test,predicted_price)\n",
    "\n",
    "print \"Optimal model has R^2 score {:,.2f} on test data\".format(r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题11 - 分析决定系数\n",
    "\n",
    "你刚刚计算了最优模型在测试集上的决定系数，你会如何评价这个结果？\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题11 - 回答\n",
    "\n",
    "决定系数是相关系数的平方，意义是变量A可以解释变量B方差的多少。这里R2指的是在最佳拟合线中可以解释的比例。上面计算出来的R2=0.8，说明有80%'MEDV'平均房价的变化可以由'RM'、'LSTAT'、'PTRATIO'三个因素的这条最佳拟合线来解释，剩余20%受其他因素影响。这个结果很不错。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 模型健壮性\n",
    "\n",
    "一个最优的模型不一定是一个健壮模型。有的时候模型会过于复杂或者过于简单，以致于难以泛化新增添的数据；有的时候模型采用的学习算法并不适用于特定的数据结构；有的时候样本本身可能有太多噪点或样本过少，使得模型无法准确地预测目标变量。这些情况下我们会说模型是欠拟合的。\n",
    "\n",
    "### 问题 12 - 模型健壮性\n",
    "\n",
    "模型是否足够健壮来保证预测的一致性？\n",
    "\n",
    "**提示**: 执行下方区域中的代码，采用不同的训练和测试集执行 `fit_model` 函数10次。注意观察对一个特定的客户来说，预测是如何随训练数据的变化而变化的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trial 1: $391,183.33\n",
      "Trial 2: $411,417.39\n",
      "Trial 3: $415,800.00\n",
      "Trial 4: $428,316.00\n",
      "Trial 5: $413,334.78\n",
      "Trial 6: $411,931.58\n",
      "Trial 7: $399,663.16\n",
      "Trial 8: $407,232.00\n",
      "Trial 9: $402,531.82\n",
      "Trial 10: $413,700.00\n",
      "\n",
      "Range in prices: $37,132.67\n"
     ]
    }
   ],
   "source": [
    "# 请先注释掉 fit_model 函数里的所有 print 语句\n",
    "vs.PredictTrials(features, prices, fit_model, client_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 12 - 回答：\n",
    "\n",
    "10次预测的结果差异都在410万左右，最大值与最小值差别为28653，误差率为7%左右，差别不大，可认为该模型足够健壮。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 13 - 实用性探讨\n",
    "*简单地讨论一下你建构的模型能否在现实世界中使用？* \n",
    "\n",
    "提示：回答以下几个问题，并给出相应结论的理由：\n",
    "- *1978年所采集的数据，在已考虑通货膨胀的前提下，在今天是否仍然适用？*\n",
    "- *数据中呈现的特征是否足够描述一个房屋？*\n",
    "- *在波士顿这样的大都市采集的数据，能否应用在其它乡镇地区？*\n",
    "- *你觉得仅仅凭房屋所在社区的环境来判断房屋价值合理吗？*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 13 - 回答：\n",
    "\n",
    "首先，在今天不适用，因为30年过去了，经济迅猛发展，人们的消费观念发生了巨大的变化。\n",
    "\n",
    "其次，根据上面的计算，数据中呈现的特征只能描述80%，不算足够，房屋的价格还和年限、家具档次等相关。\n",
    "\n",
    "再次，不能应用在其它乡镇地区，大都市的人们向往着紧张忙碌的白领生活，乡镇地区向往的是宁静祥和的生活。\n",
    "\n",
    "最后，仅仅凭房屋所在社区的环境来判断房屋价值是不合理的，房屋的价格跟房屋的质量，房屋的新旧程度，房屋的装修程度有关系。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 可选问题 - 预测北京房价\n",
    "\n",
    "（本题结果不影响项目是否通过）通过上面的实践，相信你对机器学习的一些常用概念有了很好的领悟和掌握。但利用70年代的波士顿房价数据进行建模的确对我们来说意义不是太大。现在你可以把你上面所学应用到北京房价数据集中 `bj_housing.csv`。\n",
    "\n",
    "免责声明：考虑到北京房价受到宏观经济、政策调整等众多因素的直接影响，预测结果仅供参考。\n",
    "\n",
    "这个数据集的特征有：\n",
    "- Area：房屋面积，平方米\n",
    "- Room：房间数，间\n",
    "- Living: 厅数，间\n",
    "- School: 是否为学区房，0或1\n",
    "- Year: 房屋建造时间，年\n",
    "- Floor: 房屋所处楼层，层\n",
    "\n",
    "目标变量：\n",
    "- Value: 房屋人民币售价，万\n",
    "\n",
    "你可以参考上面学到的内容，拿这个数据集来练习数据分割与重排、定义衡量标准、训练模型、评价模型表现、使用网格搜索配合交叉验证对参数进行调优并选出最佳参数，比较两者的差别，最终得出最佳模型对验证集的预测分数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO 6\n",
    "\n",
    "# 你的代码"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题14 - 北京房价预测\n",
    "你成功的用新的数据集构建了模型了吗？他能对测试数据进行验证吗？它的表现是否符合你的预期？交叉验证是否有助于提升你模型的表现？\n",
    "\n",
    "**提示：**如果你是从零开始构建机器学习的代码会让你一时觉得无从下手。这时不要着急，你要做的只是查看之前写的代码，把每一行都看明白，然后逐步构建你的模型。当中遇到什么问题也可以在我们论坛寻找答案。也许你会发现你所构建的模型的表现并没有达到你的预期，这说明机器学习并非是一项简单的任务，构建一个表现良好的模型需要长时间的研究和测试。这也是我们接下来的课程中会逐渐学到的。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题14 - 回答"
   ]
  }
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